We are required to find an equivalent expression for (4 x y minus 3 z) squared
(4 x y minus 3 z) squared is equivalent to 16 x squared y squared minus 24 x y z 9 z squared, the difference of squares
- 16 x squared y squared 9 z squared, the difference of squares = 16x²y² + 9z²
- 16 x squared y squared 9 z squared, a perfect square trinomial = 16x²y² + 9z²
- 16 x squared y squared minus 24 x y z 9 z squared, the difference of squares = 16x²y² - 24xyz + 9z²
- 16 x squared y squared minus 24 x y z 9 z squared, a perfect square trinomial = 16x²y² - 24xyz + 9z²
Given:
(4 x y minus 3 z) squared
= (4xy - 3z)²
= (4xy - 3z) (4xy - 3z)
= 16x²y² - 12xyz - 12xyz + 9z²
= 16x²y² - 24xyz + 9z²
Therefore, (4 x y minus 3 z) squared is equivalent to 16 x squared y squared minus 24 x y z 9 z squared, the difference of squares
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