Question

1. What 3 things must be true for a binomial to be a difference of squares?

2. How do you determine the square root of a term whose variable(s) have exponents greater than 2?

3. Is this a difference of squares? Show your work and explain. 64v4 − 225w10

Answer 1

See below.

Explanation:

1.

The 2 terms must be perfect squares.

One or both terms could be a constant.

The exponents could be an even number other than 2.

2.

You divide the exponent by 2.

:For example, The square root of x^4 is x^(4/2) = x^2.

3.

The general form for the difference of 2 squares is:

a^2 - b^2 = (a - b)(a + b).

So

64v^4 - 225w^10 is a difference of 2 squares:

The 2 terms have square roots 8v^2 and 15w^5 respectively.

64v^4 - 225w^10 = (8v^2 - 15w^5)(8v^2 + 15w^5).