the distributive property & combining like terms
TRANSCRIPT
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.
BACK
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
BACK
Combine like terms with parenthesis…
153238 ff
15968 ff
614 f
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