Mastery Alg 1
Reteach 8-1
8-1
Name: _________________________
Reteaching
Adding and Subtracting Polynomials
You can add and subtract polynomials by lining up like terms and then adding or
subtracting each part separately.
Problem
What is the simplified form of (3x2 – 4x + 5) + (5x2 + 2x – 8)?
3x2 – 4x + 5
+ 5x2 + 2x – 8
Write the problem vertically, lining up the like terms.
Then add each pair of like terms.
Add the x2 terms.
Solve
2
2
3x + 5x = 8x
Add the x terms.
Add the constant terms.
–4x + 2x = –2x
2
5 + (–8) = –3
3x2 – 4x + 5
+ +5x2 + 2x – 8
8x2 – 2x – 3
Check
Add the sums.
Check your solution using subtraction.
8x – 5x2 = 3x2
2
–2x – 2x = –4x
–3 – (–8) = 5
Solution: (3x2 – 4x + 5) + (5x2 + 2x – 8) = 8x2 – 2x – 3
Exercises
Simplify.
1.
5b 2  3b
 2b 2  5b
2.
4.
3e2  5e  2
 e2  2e  7
5.
7. (3h2 + 5) + (–5h2 – 3)
3c 2  3c
 4c 2  2 c
4f3 2 f 2 5f
2 f 3  4 f 2  3 f
3.
4d 2  3d  6
 2 d 3  5d  3
6.
5 g 3  2 g 2  3g
2 g 3  5 g 2  2 g
8. (2j2 + 4j – 6) + (4j2 – 3j – 3)
To subtract polynomials, follow the same steps as in addition.
Problem
What is the simplified form of (6x3 + 4x2 – 3x) – (2x3 + 3x2 – 5x)?
6x3 + 4x2–3x
– (2x3 + 3x2–5x)
Write the problem vertically, lining up the like terms.
Then subtract each pair of like terms.
Solve
Subtract the x3 terms.
6x – 2x = 4x
3
3
Subtract the x2 terms.
4x – 3x = x
3
2
2
Subtract the x terms.
–3x – (–5x) = 2x
2
6x3 + 4x2–3x
– (2x3 + 3x2–5x)
4x3 + x2 + 2x
Check
Add the differences.
Check your solution using subtraction.
4x3 + 2x3 = 6x3
2x + (–5x) = –3x
x2 + 3x2 = 4x2
Solution: (6x3 + 4x2 – 3x) – (2x3 + 3x2 – 5x) = 4x3 + x2 + 2x
Exercises
Simplify.
2
9. 4k + 5k
–3k2 + 2k
12.
10.
5p2 + 6p + 4
– (7p2 + 4p+ 8)
13.
15. (6s – 5s) – (–2s + 3s)
2
2
5m2 + 4m
–(2m2 + 3m)
3q3 + 2q2 + 7q
– (6q3 + 4q2 – 5q)
11.
7n2 + 4n + 9
– (4n2 + 3n + 5)
14.
2r3 – 2r2 + 5r
– (4r3 + 5r2 + 3r)
16. (3w + 6w – 5) – (5w – 4w + 2)
2
2