Use the distributive property of multiplication over addition to rewrite the sum as a product of two factors, where one of the factors is a sum.
A) 4(5a^2 - 4 - 2a)
B) a(20a^2 - 16a - 8)
C) 4(5a^ - 4a - 2)
D) 4a(5a - 16 - 8a)
To rewrite the given expression as a product of two factors, we need to use the distributive property of multiplication over addition. The distributive property states that for any real numbers a, b, and c, the product of a and the sum of b and c is equal to the sum of the products of a and b and a and c.
Let's go through each option to find the correct answer:
A) 4(5a^2 - 4 - 2a)
To apply the distributive property, we need to multiply 4 with each term inside the parentheses separately:
4 * 5a^2 = 20a^2
4 * -4 = -16
4 * -2a = -8a
So, the expression becomes: 20a^2 - 16 - 8a
B) a(20a^2 - 16a - 8)
Again, we need to apply the distributive property by multiplying a with each term inside the parentheses:
a * 20a^2 = 20a^3
a * -16a = -16a^2
a * -8 = -8a
The expression becomes: 20a^3 - 16a^2 - 8a
C) 4(5a^ - 4a - 2)
Here, it seems like there is a mistake in the exponent of a. Let's assume it should be a^2 instead:
4 * 5a^2 = 20a^2
4 * -4a = -16a
4 * -2 = -8
The expression becomes: 20a^2 - 16a - 8
D) 4a(5a - 16 - 8a)
Applying the distributive property to this expression, we multiply 4a with each term inside the parentheses:
4a * 5a = 20a^2
4a * -16 = -64a
4a * -8a = -32a^2
The expression becomes: 20a^2 - 64a - 32a^2
After evaluating all the options, we can see that the correct answer is B) a(20a^2 - 16a - 8), where the expression can be written as a product of two factors, with one factor being a and the other factor being the sum (20a^2 - 16a - 8).