Shri Chhatrapati Shivaji vidyalaya Akolner Tal Nagar DistA

Shri Chhatrapati Shivaji vidyalaya, Akolner. Tal- Nagar, Dist-A. Nagar. PPT- I Smt-Udmale V R. STD-7 Sub- Math

Product Of algebraic expressions

Types Of Algebraic Expressions Ø Monomial Ø Binomial Ø Trinomial

Product Of Algebraic Expressions v Multiplying one monomial by another monomial v Multiplying a binomial by a monomial v Multiplying a trinomial by a binomial

Multiplying one monomial by another monomial EX. 1. 4 x× 7 x Method 4 X× 7 X = 4 ×x× 7× x = (4× 7) × (x×x) =28 x² Explanation Write using multiplication write coefficients in one bracket and variables in another. Simplify.

EX. 2. X/2× x²/3 x/2 x/3 = x×x/2× 3 = x³/6

Multiplying a binomial by a monomial Ex. 1. Multiply 3 x×(5 x²+2 x) Method Explanation 3 x×(5 x²+2 x) Multiplied every term in the =(3 x× 5 x²) +(3 x× 2 x) bracket by the monomial =15 x²+6 x² outside it.

Ex. 2. 7× (p + q) 7× p+ 7× q 7 p+ 7 q

Multiplying a binomial by a binomial Method Horizontal arrangement (a+2 b) (3 a+5 b) =a×(3 a+5 b) + 2 b×(3 a+5 b) =3 a² +5 ab+6 ab+10 b² =3 a²+11 ab+10 b² Vertical arrangement 3 a + 5 b a + 2 b 6 ab + 10 b +3 a + 5 ab 3 a+11 ab +10 b Explanation multiplied

(a+ b) (b +d) a (b +d )+b (b +d) a×b+b×d+b×d ab +ad + b² + bd

Multiplying a trinomial by a monomial Method EX. 1. Explanation 2 x×(3 x²-x+5) Multiplied every term =(2 x× 3 x²)-(2 x×x)+(2 x× 5)inside the bracket by =6 x³-2 x²+10 x the monomial outside. Method EX. 2. Explanation (8 c-2 b+d)× 5 a Multiplied every term =(8 c× 5 a)-(2 b× 5 a)+(d× 5 a) inside the bracket by the =40 ac-10 ab+5 ab monomial outside.

Multiplying trinomial by a binomial EX. 1. (x+3) (x²+8 x-5) =x (x²+8 x-5)+3×(x²+8 x-5) =x×x²+x× 8 x-x× 5+3×x²+3× 8 x-3× 5 =x³+8 x²-5 x+3 x²+24 x-15 =x³+8 x²+3 x²+24 x-15 =x³+11 x²+19 x-15

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