Question

Which of the following is equivalent to 25x2+16−40x−64y2? Select two.

(5x+4)^2−64y^2

(5x−4)^2−64y^2

(5x−8y)^2+16

(5x−4−8y)(5x−4−8y)

(5x−4−8y)(5x+4+8y)

(5x−4−8y)(5x−4+8y)

Answer 1

The equivalent expression to the given expression 25x²+16−40x−64y² are; (5x-4)²−64y² and (5x−4−8y)(5x+4+8y)

Difference of two squares

According to the question:

• We are required to determine the equivalent expression.

When we try to factorise the given expression systematically; we have;

• 25x²+16−40x−64y² = (25x²+16−40x)−64y²

By the difference of two squares concept;

• (25x²+16−40x) = (5x-4)²

Therefore, an equivalent expression is; (5x-4)²−64y²

Similarly, (5x-4)²−64y² is the difference of two squares and can be rewritten as; (5x−4−8y)(5x+4+8y)

Hence, we have the suggested expressions as equivalent expressions.

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