Question

Which is equivalent to (4 x y minus 3 z) squared, and what type of special product is it?

Answer 1

To expand the expression (4xy - 3z)², you can use the FOIL method. The expanded expression is 16x²y² - 24xyz + 9z². This expression represents a perfect square trinomial.

Step-by-step explanation:

The expression (4xy - 3z)2 is equivalent to (4xy - 3z)(4xy - 3z). To expand the expression, we can use the FOIL method, which stands for First, Outer, Inner, Last:

1. First: Multiply the first terms in each binomial, which gives us (4xy)(4xy) = 16x2y2
2. Outer: Multiply the outer terms in each binomial, which gives us (4xy)(-3z) = -12xyz
3. Inner: Multiply the inner terms in each binomial, which gives us (-3z)(4xy) = -12xyz
4. Last: Multiply the last terms in each binomial, which gives us (-3z)(-3z) = 9z2

Combining these terms, we get the expanded expression 16x2y2 - 12xyz - 12xyz + 9z2 = 16x2y2 - 24xyz + 9z2.

It is equivalent to a special product known as a perfect square trinomial.