Question

Use the distributive property to write an equivalent expression.

1. 2(9n + 4)

2. −3(7n − 2)

3. 4(x − 9)

4. (7 + 2y)5

Answer 1

1. 2(9n + 4) --> 18x + 8

2. -3(7n - 2) --> -21n + 6

3. 4(x - 9) --> 4x - 36

4. (7 + 2y)5 --> 5(2y + 7) --> 10y + 35

Answer 2

Answers:
1. 18n+8
2. -21n+6
3. 4x-36
4. 35+10y

Step-by-step explanation:
When we apply the distributive property, we essentially take the number on the outside of the bracket and multiply it to everything on the inside.

1. 2(9n+4)
2 times 9n is 18n and 2 times 4 is 8.
18n+8

We can also solve this problem by “opening up” the brackets:
2(9n+4)
=2(9n)+2(4)
=18n+8

2. -3(7n-2)
-3 times 7n is -21n and -3 times -2 is 6 (because two negatives multiplied together make a positive).
-21n+6

-3(7n-2)
=-3(7n)-(-3)(2)
=-21n+6

3. 4(x-9)
4 times x is 4x and 4 times 9 is 36.
4x-36

4(x-9)
=4(x)-4(9)
=4x-36

4. (7+2y)5
The same concept applies here. The number on the outside of the bracket is now at the end, but it doesn’t change the way we solve it.
5 times 7 is 35 and 5 times 2y is 10y.
35+10y

(7+2y)5
=5(7)+5(2y)
=35+10y

I hope this helps!