Algebra 1 · Unit 7
Find sums and differences of polynomials using like terms, a minus distributed, and tile pictures.
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Like terms
Add or subtract the coefficients of matching powers. x² and x are not like terms.
Subtract means distribute a minus
Change every sign in the polynomial you are subtracting, then combine.
Hands-on and pictures
Algebra tiles: same-size tiles combine. A zero pair is one positive tile with one negative tile of the same size.
Degree stays
Adding does not raise the degree. Canceling the leading terms can lower it.
Add two trinomials. Integer coefficients.
2x² + x² = 3x²
3x + 4x = 7x
1 + 5 = 6
3x² + 7x + 6
Answer: 3x² + 7x + 6
6x + 4
Answer: 6x + 4
4x² + 3
Answer: 4x² + 3
7x² + 3
Answer: 7x² + 3
Distribute the minus.
5x − 2 − 3x − 1
2x − 3
Answer: 2x − 3
7 tiles of that size.
7x
Answer: 7x
Subtract a trinomial, or a missing term.
Distribute the minus.
5x² − 2x + 1 − 2x² − 3x + 4
3x² − 5x + 5
Answer: 3x² − 5x + 5
3x² + x − x² + 4x − 2
2x² + 5x − 2
Answer: 2x² + 5x − 2
5x³ − 3x + 5
Answer: 5x³ − 3x + 5
−4x + 10
Answer: −4x + 10
(3x + 2) − x = 2x + 2
Answer: 2x + 2
2x² + 8
Answer: 2x² + 8
More terms, or a subtraction that cancels the quadratic.
2x³ − x² + 4x − 1 − x³ + 3x² − x − 5
x³ + 2x² + 3x − 6
Answer: x³ + 2x² + 3x − 6
6x
Answer: 6x
p − 4 = −1
p = 3
Answer: p = 3
x² + 4x + 2
Answer: x² + 4x + 2
3x + 2 + x − 5 − 4x + 1
−2
Answer: −2
(x + 1)² = x² + 2x + 1
Subtracting the same polynomial leaves 0.
The tiles for a square of side x + 1 are exactly x² + 2x + 1.
Answer: 0
Either order gives 4x + 1.
Commutative property of addition on like terms.
Answer: 4x + 1 either order
(x² + 5x + 6) − (x + 2) = x² + 4x + 4
(x + 2) + (x² + 4x + 4) = x² + 5x + 6
Answer: x² + 4x + 4
The 3 must change sign too: − (2x − 3) = −2x + 3.
5x − 1 − 2x + 3 = 3x + 2
Answer: 3x + 2
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