Distribution and like terms

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Distribution and like terms
A look at the algebra
behind algebra tiles….
Combining like terms
When combining like terms, add the coefficients on each group of like terms.
Example 1:
With algebra tiles
6x + 5 + 2x
6x + 5 + 2x
With algebra
6x + 5 + 2x
Identify
like terms.
(6 + 2)x + 5
Add the
coefficients
on like terms.
8x + 5
8 positive x-bars and 5 positive units
8x + 5
Simplify.
Example 2:
9x + 4 – 2x
9x + 4 + -2x
With algebra tiles
9x + 4 – 2x
Algebraically
9x + 4 – 2x
Identify
like terms.
(9 + -2)x + 4
Combine the
coefficients
on like terms.
7x + 4
7 positive x-bars and 4 positive units
7x + 4
Simplify.
Example 3:
6x + 5 + -3x + -8
With algebra tiles
6x + 5 + -3x + -8
3 positive x-bars and 3 negative units
3x + -3
3x – 3
Algebraically
6x + 5 + -3x + -8
Identify
like terms.
(6 + -3)x + (5 + -8)
Add the
coefficients
on like terms.
3x + -3
3x – 3
Simplify.
Distribution
Multiply the term outside the parentheses by each term inside the parentheses.
Example 4:
With algebra tiles
3(x + 5)
Build 3 groups
of 1x + 5.
3(x + 5)
Algebraically
3(x + 5)
Distribute.
3(x) + 3(5)
Multiply.
3x + 15
3 positive x-bars and 15 positive units
3x + 15
Simplify.
Example 5:
2(3x – 1)
With algebra tiles
2(3x + -1)
Algebraically
Build 2 groups of 3x + -1.
2(3x + -1)
2(3x) + 2(-1)
6 positive x-bars and 2 negative units
6x + -2 = 6x – 2
6x + -2
6x – 2
Distribute.
Multiply.
Simplify.
Example 6:
2(x2 – 2x + 1)
With algebra tiles
2(x2 + -2x + 1)
Algebraically
Build 2 groups of x2 + -2x + 1.
2(x2 + -2x + 1)
2(x2) + 2(-2x) + 2(1)
2 positive x2 tiles, 4 negative x-bars,
and 2 positive units
2x2 + -4x + 2 = 2x2 – 4x +
2x2 + -4x + 2
2x2 – 4x + 2
2
Distribute.
Multiply.
Simplify.
Distribution and combining like terms
Example 7:
4(2x + 5) – 8
4(2x + 5) + -8
4(2x) + 4(5) + -8
8x + 20 + -8
8x + (20 + -8)
8x + 12
Distribution first.
Identify like terms.
Combine like terms.
Simplify.
Example 8:
-4 + 5(2x + 3) + x
-4 + 5(2x + 3) + x
-4 + 5(2x) + 5(3) + 1x
-4 + 10x + 15 + 1x
(10 + 1)x + (-4 + 15)
11x + 11
Distribution first.
Identify like terms.
Combine like terms.
Simplify.

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