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Math 9
MOM Page 329
Lesson 22(2)
Name SOLUTIONS
8. Simplify
a) (6x + 2) + (3x + 4) b) (5a – 3) + (2a + 7 ) c) (8 – 4m) + (-3 – 2m) d) (-x + 4) + (7x – 2)
e) (4n2 – 3n – 1) + (2n2 – 5n -3) f) (3x2 + 6x – 8) + (-5x2 – x + 4)
g) (2 – 3c + c2) + (5 – 4c – 4c2) h) (8 – 2n – n2) + (-3 – n + 4n2)
i) (ab + 3b – 5) + (2ab – 4b – 6) j) (mn – 5m – 2) + (-6n + 3m + 7)
(6x + 2) + (3x + 4)
6x + 3x + 2 + 4
9x + 6
(-x + 4) + (7x – 2)
-x + 7x + 4 – 2
6x + 2
(5a – 3) + (2a + 7)
5a + 2a – 3 + 7
7a + 4
(4n2 – 3n – 1) + (2n2 – 5n -3)
4n2 + 2n2 – 3n – 5n – 1 – 3
6n2 – 8n - 4
(8 – 4m) + (-3 – 2m)
-4m – 2m + 8 – 3
-6m + 5
(3x2 + 6x – 8) + (-5x2 – x + 4)
3x2 – 5x2 + 6x – x – 8 + 4
-2x2 + 5x - 4
(2 – 3c + c2) + (5 – 4c – 4c2)
c2 – 4c2 – 3c – 4c + 2 + 5
-3c2 – 7c + 7
(mn – 5m – 2) + (-6n + 3m + 7)
mn – 5m + 3m – 6n – 2 + 7
mn – 2m – 6n + 5
(8 – 2n – n2) + (-3 – n + 4n2)
-n2 + 4n2 – 2n – n + 8 – 3
3n2 – 3n + 5
(ab + 3b – 5) + (2ab – 4b – 6)
ab + 2ab + 3b – 4b – 5 – 6
3ab – b - 11
10. Simplify
a) (-2x + 3) – (3x + 2) b) (4 – 5n) – (-6n + 2) c) (8a2 + 2a – 3) – (-6a2 + 4a + 7)
d) (-6x2 + 5x + 1) – (4x2 + 5 – 2x)
e) (3 – 2m – n2) – (7 – 6m + n2)
f) (2 + 6x2) – (7 – 3x2) g) (5 – 6t2) – (3 – t2) h) (5x2 – 3x) – (-3x + 5x2)
(-2x + 3) – (3x + 2)
-2x + 3 – 3x – 2
-2x – 3x + 3 – 2
-5x + 1
(-6x2 + 5x + 1) – (4x2 + 5 – 2x)
-6x2 + 5x + 1 – 4x2 – 5 + 2x
-6x2 – 4x2 + 5x + 2x + 1 – 5
-10x2 + 7x - 4
(5 – 6t2) – (3 – t2)
(4 – 5n) – (-6n + 2)
4 – 5n + 6n – 2
-5n + 6n + 4 – 2
n+2
(3 – 2m – n2) – (7 – 6m + n2)
3 – 2m – n2 – 7 + 6m – n2
-n2 – n2 – 2m + 6m + 3 – 7
-2n2 + 4m - 4
(5x2 – 3x) – (-3x + 5x2)
(8a2 + 2a – 3) – (-6a2 + 4a + 7)
8a2 + 2a – 3 + 6a2 – 4a – 7
8a2 + 6a2 + 2a – 4a – 3 – 7
14a2 – 2a - 10
(2 + 6x2) – (7 – 3x2)
2 + 6x2 – 7 + 3x2
6x2 + 3x2 + 2 – 7
9x2 - 5
5 – 6t2 – 3 + t2
-6t2 + t2 + 5 – 3
-5t2 + 2
5x2 – 3x + 3x – 5x2
5x2 – 5x2 – 3x + 3x
0
11. Simplify.
a) (3x – 2) – (x – 1) b) (2a + 3) + (6a – 1) c) (5x2 – 3x) – (x2 + 2x) d) (5t – 4) + (3t – 1)
e) (3 – 4x + x2) – (2x – x2) f) (3n2 – 6n + 5) – (3n2 – 2n – 1)
(3x – 2) – (x – 1)
3x – 2 – x + 1
3x – x – 2 + 1
2x - 1
(5t – 4) + (3t – 1)
5t – 4 + 3t – 1
5t + 3t – 4 – 1
8t - 5
(2a + 3) + (6a – 1)
2a + 3 + 6a – 1
2a + 6a + 3 – 1
8a + 2
(3 – 4x + x2) – (2x – x2)
3 – 4x + x2 – 2x + x2
x2 + x2 – 4x – 2x + 3
2x2 – 6x + 3
(5x2 – 3x) – (x2 + 2x)
5x2 – 3x – x2 – 2x
5x2 – x2 – 3x – 2x
4x2 – 5x
(3n2 – 6n + 5) – (3n2 – 2n – 1)
3n2 – 6n + 5 – 3n2 + 2n + 1
3n2 – 3n2 – 6n + 2n + 5 + 1
-4n + 6
13. a) What polynomial sum do the tiles represent?
(-2x2 + 5x – 3 ) + (x2 + x + 7)
-2x2 + x2 + 5x + x – 3 + 7
-x2 + 6x + 4
b) Explain how to use the algebra tiles to simplify the sum of the polynomials in part a.
If you use the zero effect – meaning crossing out every one positive with one negative
and then adding up what is left.
Math 9
MOM Page 330
Lesson 22(2)
14. Explain why the two polynomials are not opposites.
a) 5x2 – 3x – 2 and 5x2 + 3x + 2
b) x2 + 7x – 9 and –x3 – 7x + 9
c) -4y + y2 + 11 and 4y – y2 + 11
d) x3 – 4x2 + 9 and –x3 + 4x2 – x
Because 5x2 should be -5x2
Because –x3 should be –x2
Because + 11 should be -11
Because –x should be + 9
16. Simplify.
a) (3x2 – 2x + 4) + (x2 + 3)
b) (3x2 – 2x + 4) – (x2 + 3) c) (5m – 2m2) + (m2 – 6)
d) (5m – 2m2) – (m2 – 6)
(3x2 – 2x + 4) + (x2 + 3)
3x2 – 2x + 4 + x2 + 3
3x2 + x2 – 2x + 4 + 3
4x2 – 2x + 7
(5m – 2m2) + (m2 – 6)
5m – 2m2 + m2 – 6
-2m2 + m2 + 5m - 6
(3x2 – 2x + 4) – (x2 + 3)
3x2 – 2x + 4 – x2 – 3
3x2 – x2 – 2x + 4 – 3
2x2 – 2x + 1
(5m – 2m2) – (m2 – 6)
17. Simplify. Find the value of the polynomial when : i) x = 1, ii) x = -2.
a) (1 – 2x2 – x) + (2x – 3x2 – 7)
(1 – 2x2 – x) + (2x – 3x2 – 7)
1 – 2x2 – x + 2x – 3x2 – 7
-2x2 – 3x2 – x + 2x + 1 – 7
-5x2 + x – 6
-5(1)2 + (1) – 6
-5 + 1 – 6
-10
-5x2 + x – 6
-5(-2)2 + (-2) – 6
-5(4) – 2 – 6
-20 – 8
-28
b) (3 – 2x2 – x) – (2x – 3x2 – 7)
(3 – 2x2 – x) – (2x – 3x2 – 7)
3 – 2x2 – x – 2x + 3x2 + 7
-2x2 + 3x2 – x – 2x + 3 + 7
x2 – 3x + 10
(1)2 – 3(1) + 10
1 – 3 + 10
8
x2 – 3x + 10
(-2)2 – 3(-2) + 10
4 + 6 + 10
20
19. Simplify.
a) (3x2 – 7x + 4) + (5x – 7x2 + 6)
b) (6 – 3x + x2) + (9 – x)
c) (1 – 7x2 + 2x) + (x3 – 3x2 + 7)
d) (5x – x2) + (3x + x2 – 7)
(3x2 – 7x + 4) + (5x – 7x2 + 6)
3x2 – 7x + 4 + 5x – 7x2 + 6
3x2 – 7x2 – 7x + 5x + 4 + 6
-4x2 – 2x + 10
(1 – 7x2 + 2x) + (x3 – 3x2 + 7)
1 – 7x2 + 2x + x3 – 3x2 + 7
x3 – 7x2 – 3x2 + 2x + 1 + 7
x3 – 10x2 + 2x + 8
(6 – 3x + x2) + (9 – x)
6 – 3x + x2 + 9 – x
x2 – 3x – x + 6 + 9
x2 – 4x + 15
(5x – x2) + (3x + x2 – 7)
5x – x2 + 3x + x2 – 7
-x2 + x2 + 5x + 3x – 7
8x - 7
20. Simplify.
a) (5x2 + 7x + 9) – (3x2 + 4x + 2)
b) (11m2 – 5m + 8) – (7m2 + m – 3)
c) (4a2 – 3a3 – 7) – (a2 – 2a3 – 13)
d) (-6x2 + 17x – 4) – (3x2 + 12x + 8)
(5x2 + 7x + 9) – (3x2 + 4x + 2)
5x2 + 7x + 9 – 3x2 – 4x – 2
5x2 – 3x2 + 7x – 4x + 9 – 2
2x2 + 3x + 7
(4a2 – 3a3 – 7) – (a2 – 2a3 – 13)
4a2 – 3a3 – 7 –a2 + 2a3 + 13
-3a3 + 2a3 + 4a2 – a2 – 7 + 13
-a3 + 3a2 + 6
(11m2 – 5m + 8) – (7m2 + m – 3)
11m2 – 5m + 8 – 7m2 – m + 3
11m2 – 7m2 -5m – m + 8 + 3
4m2 – 6m + 11
(-6x2 + 17x – 4) – (3x2 + 12x + 8)
-6x2 + 17x – 4 – 3x2 – 12x – 8
-6x2 – 3x2 + 17x – 12x – 4 – 8
-9x2 + 5x - 12
21. a) Simplify.
i)
ii)
(5 – 2m – m2) – (7m + 4 – 5m2)
(x2 – 4x + x3) – (3x + 5 – x3)
c) Find the value of each polynomial in part a when m = -2.
(5 – 2m – m2) – (7m + 4 – 5m2)
5 – 2m – m2 – 7m – 4 + 5m2
-m2 + 5m2 -2m – 7m + 5 – 4
4m2 – 9m + 1
4(-2)2 – 9(-2) + 1
4(4) + 18 + 1
16 + 19
35
(x2 – 4x + x3) – (3x + 5 – x3)
x2 – 4x + x3 – 3x – 5 + x3
x3 + x3 + x2 – 4x – 3x – 5
2x3 + x2 – 7x – 5
2(-2)3 + (-2)2 – 7(-2) – 5
2(-8) + 4 + 14 – 5
-16 + 18 – 5
-3
22. Simplify.
i)
ii)
(y2 – 2y) – (5 – 2y)
(8y – 5) – (y – 4) + (3y + 1)
b) Find the value of each polynomial in part a when y = 4.
(y2 – 2y) – (5 – 2y)
y2 – 2y – 5 + 2y
y2 – 2y + 2y – 5
y2 – 5
(4)2 – 5
16 – 5
11
(8y – 5) – (y – 4) + (3y + 1)
8y – 5 – y + 4 + 3y + 1
8y – y + 3y – 5 + 4 + 1
10y
10(4)
40