Download 1-4 Distributive Property

Goal: Use the distributive property to
evaluate and simplify expressions.
Distributive Property - Multiplying a term
outside parenthesis by all terms inside
parenthesis.
2(x + 5) = 2(x) + 2(5) = 2x + 10
(x + 5)2 =(x)2 + (5)2 = 2x + 10
Remember that a factor must multiply each term
of anDISTRIBUTIVE
expression. PROPERTY
THE
(–3)(1 + x) = (–3)(1) + (–3)(x)
= –3 – 3x
(y – 5)(–2) = (y)(–2) + (–5)(–2)
= –2y + 10
–(7 – 3x) = (–1)(7) + (–1)(–3x)
= –7 + 3x
Forgetting to distribute the negative sign when
multiplying by a negative factor is a common error.
1.
3(x + 7)
= 3x + 21
2.
-5(y + 6)
= -5y – 30
3.
4x(3x – 8)
= 12x2 – 32x
4.
(6x – 5)(-12)
= -72x + 60
5.
4(y2 + 8y + 2)
= 4y2 + 32y + 8
Simplify 6(x – 4).
A. 6x – 4
B. 6x – 24
C. x – 24
D. 6x + 2
Simplify 3(x3 + 2x2 – 5x + 7).
A. 3x3 + 2x2 – 5x + 7
B. 4x3 + 5x2 – 2x + 10
C. 3x3 + 6x2 – 15x + 21
D. x3 + 2x2 – 5x + 21
5x + 3(2x – 7)
 Distribute
5x + 3(2x) + 3(-7)
 Multiply
5x + 6x – 21
 Combine
11x – 21
Terms
Like
3 – 2(4 + x)
3 + (–2)(4 + x)
3 + [(–2)(4) + (–2)(x)]
3 + (–8) + (–2x)
–5 + (–2x)
–5 – 2x
 Turn
problem into an
addition problem.
 Distribute
 Multiply
 Combine
 Rewrite
Like Terms
1.
4(2x – 3) + 7x
= 15x – 12
2.
2 + 6(-4x + 8)
= -24x + 50
3.
5x – 4(3x – 9)
= -7x + 36
4.
6x(3x – 8) + 12x
= 18x2 – 36x
Simplify the expression 3(2x – y) + 2(4x + y).
A. 2x + 4y
B. 11x
C. 14x – y
D. 12x + y
1.
Twice the difference of 3x and y increased
by five times the sum of x and 2y.
11x + 8y
2.
Six times the sum of x and y increased by
four times the difference of 5x and y.
26x + 2y
Use the expression three times the difference of 2x
and y increased by two times the sum of 4x and y.
Write an algebraic expression for the verbal
expression.
A. 3(2x + y) + 2(4x – y)
B. 3(2x – y) + 2(4x + y)
C. 2(2x – y) + 3(4x + y)
D. 3(x – 2y) + 2(4x + y)

On whiteboards
 Pages
29-30 #25-28, 33-39, 46, 47