Multiplying Polynomials Intermediate Algebra Multiply monomial by polynomial

Multiplying Polynomials Intermediate Algebra

Multiply monomial by polynomial

Multiply polynomial by polynomial

Multiply two binomials

Multiply two binomials FOIL

Multiply two binomials F FOIL

Multiply two binomials FOIL O F

Multiply two binomials FOIL O F I

Multiply two binomials FOIL O F I L

Multiply the Sum and the Difference of Two Terms

Squaring a Binomial (a+b)²=a²+2 ab+b² (a-b)²=a²-2 ab+b²

Squaring a Binomial (a+b)²=a²+2 ab+b²

Squaring a Binomial (a-b)²=a²-2 ab+b²

1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 18 a²b – 2 ab 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 4 a² – 16 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 4 a² – 16 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• n² + 36 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• n² + 36 Prime! 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² = ( )² + 2( )( ) +( )² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² = (5 a)² + 2( )( ) +(b)² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² = (5 a)² + 2(5 a)(b) +(b)² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 25 a² + 10 ab + b² = (5 a)² + 2(5 a)(b) +(b)² = (5 a + b)² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = = (2 a)³ + (5)³ 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = = (2 a)³ + (5)³ =(2 a + 5)(4 a² - 10 a + 25) 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = = (2 a)³ + (5)³ =(2 a + 5)(4 a² - 10 a + 25) (2 a)² (5)² 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• 8 a³ + 125 = = (2 a)³ + (5)³ =(2 a + 5)(4 a² - 10 a + 25) (2 a)² (5)² (2 a)(5) 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• x² - 5 x +6 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• x² - 5 x +6 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• x² - 5 x +6 = (x )(x 6 -5 ) 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• x² - 5 x +6 = (x )(x 6 -2 -3 -5 ) 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

• x² - 5 x +6 = (x – 2)(x – 3) 6 -2 -3 -5 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

xy – 6 x +7 y – 42 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

xy – 6 x +7 y – 42 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

x 6 x² - 7 x - 5 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

x 6 x² - 7 x - 5 = BOX! Always factor completely!

x 6 x² - 7 x - 5 = 3 x 2 x 6 x² -5

6 x² - 7 x - 5 = 3 x 2 x 1 -5 6 x² -5

x 6 x² - 7 x - 5 = 2 x 1 3 x -5 6 x² - 10 x 3 x -5

6 x² - 7 x - 5 = 2 x 1 3 x -5 6 x² - 10 x 3 x -5 - 10 x + 3 x = - 7 x

6 x² - 7 x - 5 = (2 x + 1)(3 x - 5) 2 x 3 x -5 6 x² - 10 x 3 x -5 1 - 10 x + 3 x = - 7 x

(3 x - 5)² - 6(3 x - 5) + 9 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+ ab + b²) a³ + b³ = (a + b)(a²- ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!

(3 x - 5)² - 6(3 x - 5) + 9 = 1. GCF (if any) 2. a² - b² = (a - b)(a + b) a³ - b³ = (a - b)(a²+2 ab + b²) a³ + b³ = (a + b)(a²-2 ab + b²) 3. a² + 2 ab + b² = (a + b)² a² - 2 ab + b² = (a - b)² x² + bx + c = (x + m)(x + n), where mn = c, and m + n = b 4. If 4 or more terms, try to factor by Grouping Always factor completely!