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Which is equivalent to (4xy – 3z)2, and what type of special product is it?

16x2y2 + 9z2, the difference of squares
16x2y2 + 9z2, a perfect square trinomial
16x2y2 – 24xyz + 9z2, the difference of squares
16x2y2 – 24xyz + 9z2, a perfect square trinomial

Respuesta :

caylus
Hello,

Answer D
16x²y²-24xyz+9z² a perfect square trinomial  which
le square of the difference of 3z from 4xy.

Answer:

[tex]16x^2y^2-24xyz +9z^2[/tex]

Step-by-step explanation:

[tex](4xy - 3z)^2[/tex]

Given expression has exponent 2, so we multiply it twice

[tex](4xy - 3z)(4xy-3z)[/tex]

Apply FOIL method to multiply the parenthesis

multiply 4xy inside the second parenthesis

and multiply -3z inside the second parenthesis

[tex]4xy(4xy-3z)=16x^2y^2-12xyz[/tex]

[tex]-3z(4xy-3z)=-12xyz+9z^2[/tex]

[tex]16x^2y^2-12xyz-12xyz+9z^2[/tex]

Combine like terms

[tex]16x^2y^2-24xyz +9z^2[/tex]