Question

date ____ sec __ name ____
homework - distributive property & combining like terms
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use distributive property to simplify each expression. easy to medium problems.

1. $7(1 - 8n)$
2. $-8(b + 3)$
3. $-6(9 - 9v)$
4. $-(3x - 9)$
5. $-9(n + 6)$
6. $-10(a + 2)$
7. $(5k - 10)\cdot -9$
8. $-4(4 + 3p)$

use distributive property and combining like terms to simplify each expression. easy to medium problems.

1. $-6(x + 2) - 2$
2. $4n - (7 - 6n)$
3. $-3 - 7(-3 - 6v)$
4. $-5(a - 6) + 2a$

use distributive property and combining like terms to simplify each expression. medium problems.

1. $7(5n - 8) + 6(4 + 6n)$
2. $-(3a + 2) - 3(5a + 7)$
3. $-5(1 + 2k) - 8(-4 + 5k)$
4. $5(-3p + 7) + 5(p - 1)$
5. $-5(x + 2) + 5(x - 5)$
6. $-4(1 - 8n) - 4(8n + 4)$

use distributive property and combining like terms to simplify each expression. challenging problems.

1. $9(m + 8) + 11(3m + 4)$
2. $11(8r + 3) - 2(-9 + 6r)$
3. $7(-12x - 3) + 10(6x + 7)$
4. $-9(1 - 10n) - 2(3n + 9)$

Explanation:

1. Simplify $-(3x - 9)$

Distribute -1: $-3x + 9$

5) Simplify $-9(n + 6)$

Distribute -9: $-9n - 54$

6) Simplify $-10(a + 2)$

Distribute -10: $-10a - 20$

7) Simplify $(5k - 10) - 9$

Combine constants: $5k + (-10 - 9) = 5k - 19$

8) Simplify $-4(4 + 3p)$

Distribute -4: $-16 - 12p$

9) Simplify $-6(x + 2) - 2$

Distribute -6: $-6x - 12 - 2$; combine constants: $-6x -14$

10) Simplify $4n - (7 - 6n)$

Distribute -1: $4n -7 +6n$; combine like terms: $10n -7$

11) Simplify $-3 -7(3 -6v)$

Distribute -7: $-3 -21 +18v$; combine constants: $18v -24$

12) Simplify $-5(a -6) +2a$

Distribute -5: $-5a +30 +2a$; combine like terms: $-3a +30$

13) Simplify $7(5n -8) +6(4 +6n)$

Distribute: $35n -56 +24 +36n$; combine terms: $71n -32$

14) Simplify $-(3a +2) -3(5a +7)$

Distribute: $-3a -2 -15a -21$; combine terms: $-18a -23$

15) Simplify $-5(1 +2k) -8(4 +5k)$

Distribute: $-5 -10k -32 -40k$; combine terms: $-26k -37$

16) Simplify $5(-3p +7) +5(p -1)$

Distribute: $-15p +35 +5p -5$; combine terms: $-10p +30$

17) Simplify $-5(x +2) +5(x -5)$

Distribute: $-5x -10 +5x -25$; $x$-terms cancel: $-35$

18) Simplify $-4(1 -8n) -4(8n +4)$

Distribute: $-4 +32n -32n -16$; $n$-terms cancel: $-32$

19) Simplify $9(m +8) +11(13m +4)$

Distribute: $9m +72 +143m +44$; combine terms: $142m +116$

20) Simplify $11(8r +3) -2(-9 +6r)$

Distribute: $88r +33 +18 -12r$; combine terms: $76r +51$

21) Simplify $7(-12x -3) +10(6x +7)$

Distribute: $-84x -21 +60x +70$; combine terms: $-24x +91$

22) Simplify $-9(1 -10n) -2(3n +9)$

Distribute: $-9 +90n -6n -18$; combine terms: $84n -27$

Answer:

1. Simplify $-(3x - 9)$

Distribute -1: $-3x + 9$

5) Simplify $-9(n + 6)$

Distribute -9: $-9n - 54$

6) Simplify $-10(a + 2)$

Distribute -10: $-10a - 20$

7) Simplify $(5k - 10) - 9$

Combine constants: $5k + (-10 - 9) = 5k - 19$

8) Simplify $-4(4 + 3p)$

Distribute -4: $-16 - 12p$

9) Simplify $-6(x + 2) - 2$

Distribute -6: $-6x - 12 - 2$; combine constants: $-6x -14$

10) Simplify $4n - (7 - 6n)$

Distribute -1: $4n -7 +6n$; combine like terms: $10n -7$

11) Simplify $-3 -7(3 -6v)$

Distribute -7: $-3 -21 +18v$; combine constants: $18v -24$

12) Simplify $-5(a -6) +2a$

Distribute -5: $-5a +30 +2a$; combine like terms: $-3a +30$

13) Simplify $7(5n -8) +6(4 +6n)$

Distribute: $35n -56 +24 +36n$; combine terms: $71n -32$

14) Simplify $-(3a +2) -3(5a +7)$

Distribute: $-3a -2 -15a -21$; combine terms: $-18a -23$

15) Simplify $-5(1 +2k) -8(4 +5k)$

Distribute: $-5 -10k -32 -40k$; combine terms: $-26k -37$

16) Simplify $5(-3p +7) +5(p -1)$

Distribute: $-15p +35 +5p -5$; combine terms: $-10p +30$

17) Simplify $-5(x +2) +5(x -5)$

Distribute: $-5x -10 +5x -25$; $x$-terms cancel: $-35$

18) Simplify $-4(1 -8n) -4(8n +4)$

Distribute: $-4 +32n -32n -16$; $n$-terms cancel: $-32$

19) Simplify $9(m +8) +11(13m +4)$

Distribute: $9m +72 +143m +44$; combine terms: $142m +116$

20) Simplify $11(8r +3) -2(-9 +6r)$

Distribute: $88r +33 +18 -12r$; combine terms: $76r +51$

21) Simplify $7(-12x -3) +10(6x +7)$

Distribute: $-84x -21 +60x +70$; combine terms: $-24x +91$

22) Simplify $-9(1 -10n) -2(3n +9)$

Distribute: $-9 +90n -6n -18$; combine terms: $84n -27$