Math home work please help me out with this

Question

Distributive property:

8(x+7)=

8(x+1)

Factor each expression

8+16=

63+81=

32+16x=

Pleas help me with this

Answer 1

Distributive property:

8(x+7)= 8X + (8)(7) = 8X + 56

8(x+1) = 8X + (8)(1) = 8X + 8

Factor each expression:

8+16= 8(1 + 2)

CHECKING: 8 + 16 = 24

8(1 + 2) = (8)(1) + (8)(2) = 8 + 16 = 24

8(1 + 2) = (8)(3) = 24

63+81= 9(7 + 9)

CHECKING: 63 + 81 = 144

9(7 + 9) = (9)(7) + (9)(9) = 63 + 81 = 144

9(7 + 9) = (9)(16) = 144

32+16x= 16(2 + X)

Hope this helps.

Answer 2

Hello!

Let's start with the Distributive Property.

The Distributive Property says that multiplying a number by a group of numbers is the same as multiplying everything out, one by one.

In other words, a(b+c) = ab + ac .

Multiply the number outside of the parentheses by all of the numbers inside of the parentheses.

In the problem 8(x+7), we need to distribute the 8 to all of the terms inside of the parentheses.

In other words, our multiplication will look like this:

1. 8 * x
2. 8 * 7

To piece it together, we simply evaluate.

8 * x = 8x

8 * 7 = 56

Now, what operation goes between these two terms? We simply look at the sign of the terms. 56 is positive, so we join them with addition.

In the end, our answer is: 8x+56 .

Let's repeat the same steps for the next problem, 8(x+1):

1. 8 * x = 8x
2. 8 * 1 = 8
3. 8(x+1) = 8x + 8

Great, now let's move on to factoring!

The key to factoring expressions is to find the greatest common factor. Once we find the GCF, we can find how many times the GCF goes into each term in the expression.

In the problem, 8+16, the GCF is 8. Now, we divide each term by the GCF:

1. 8 ÷ 8 = 1
2. 16 ÷ 8 = 2

Now, we write our answer in the format: GCF(Quotient 1 + Quotient 2). Again, if your quotient is negative, the addition will become subtraction.

Our final answer is: 8(1+2) .

Let's repeat these steps for the rest of the problems:

63 + 81

1. GCF = 9
2. 63 ÷ 9 = 7
3. 81 ÷ 9 = 9
4. 63 + 81 = 9(7+9)

32 + 16x

1. GCF = 16
2. 32 ÷ 16 = 2
3. 16x ÷ 16 = 1x
4. 32 + 16x = 16(2+x)

I hope you found this response helpful! If you have any further questions, or need more clarification, please feel free to message me!