Question

Which binomial is equivalent to (4x + y2)(4x − y2)? a) (16x² - y⁴)

b) (16x² + y⁴)
c) (16x² - y²)
d) (16x² + y²)

Answer 1

To expand the given binomials, we can use the FOIL method. By multiplying the corresponding terms of the binomials, we can determine the equivalent binomial. In this case, the equivalent binomial is (16x^2 - y^4), which is found in option a.

Step-by-step explanation:

To find the product of two binomials, we use the FOIL method. FOIL stands for First, Outer, Inner, and Last, which refers to the order in which we multiply the terms. So, let's apply the FOIL method to the given binomials:

(4x + y2)(4x - y2)

First terms: 4x * 4x = 16x2

Outer terms: 4x * -y2 = -4x * y2 = -4xy2

Inner terms: y2 * 4x = 4x * y2 = 4xy2

Last terms: y2 * -y2 = -y2 * y2 = -y4

Now, combine the like terms:

16x2 - 4xy2 + 4xy2 - y4 = 16x2 - y4

So, the equivalent binomial is (16x2 - y4), which is option a.