Distributive Property Combining Like Terms Solving Equations with

Distributive Property, Combining Like Terms, Solving Equations with Variables on Both Sides

Distributive Property n An algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. 2 (3 + 6)

6(2+4 x) n n The two terms inside the parentheses cannot be added because they are not like terms. Therefore, 2 + 4 x, the expression inside the parentheses, cannot be simplified any further. Therefore, we must distribute the 6 across the parentheses!

-(3 + x 2) n Change each positive or negative sign of the terms that were inside the parentheses. Negative or minus signs become positive or plus signs.

Try Some Yourself! n 9(x + 9) n 2(4 + 9 x) n 7(x + -1) n 12(a + b + c) n -10(3 + 2 + 7 x)

Combining Like Terms n n Term n Number, variable, or product/quotient of numbers and variables (Ex: 5, m, 2 x²) Like Terms n Terms with the same variable AND exponent

Combining Like Terms n To simplify expressions with like terms, add or subtract the coefficients. 4 k + 5 k = 9 k

Combining Like Terms n 2 ab + 6 ba n Can you add the following? 3 x³y + 2 xy³

Try It Yourself! 1) -x + 3 y – 2 x + y + 4 + 5 x -1 2) 5 a – 3 b + 12 – a + 3 – 14 b 3) 3 x + 2 m – 14 x + 2 x – 4 m + 4 - 2

Solving Equations with Variables on Both Sides n If you had this equation, how would you move the 7 to the other side of the equation? 3 x + 3 = x + 7

n How would you move the x from the left side to the right side? 3 x + 3 = x + 7 Exactly the same way you moved the seven!

n Once you subtract the x from both sides, the equation becomes a two-step equation! 2 x + 3 = 7

Try This One on Your Own! 4 x + 7 = 2 x -1

Another One! -2 x – 10 = -9 x + 11