The Distributive Property & Combining Like Terms

THE DISTRIBUTIVE PROPERTY

a(b + c) = ab + ac

(b + c)a = ba + ca

2(x + 5) 2(x) + 2(5) 2x + 10

(x + 5)2 (x)2 + (5)2 2x + 10

(1 + 5x)2 (1)2 + (5x)2 2 + 10x

y(1 + x) y(1) +y(x) y + xy

USING THE DISTRIBUTIVE PROPERTY

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The product of a and (b + c):

BACK

–(y – 5) = (y)(–1) + (–5)(–1)= –y + 5

–(7 – 3x) = (–1)(7) + (–1)(–3x)

= –7 + 3x

= –3 – 3x(–3)(1 + x)= (–3)(1) + (–3)(x)

Simplify.

Distribute the –3.

Simplify.

Distribute the –1. Simplify.

–a = –1 • a

USING THE DISTRIBUTIVE PROPERTY

Remember that a factor must multiply each term of an expression.

Forgetting to distribute the negative sign when multiplying by a negative factor is a common error.

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Like Terms are expressions that contain the same variable raised to the same power like 4mn and 7mn.

Combine like terms.

SIMPLIFYING BY COMBINING LIKE TERMS

4x2 + 2 + x2 - 6 =

11x +y The 8x and 3x are like terms and can be combined.

8x + 3x + y =

4x2 +1 x2 + 2 - 6 Group like terms.

= 5x2 - 4

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Combine like terms with parenthesis…

153238 ff

15968 ff

614 f

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