Question

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Answer 1

Answer:

(4x^2)^2 - 2(4x^2)(9y^2) +(9y^2)^2

(4x^2 - 9y^2)

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Answer 2

Answer:

Hi

Step-by-step explanation:

((16×(x⁴))-((72×(x²))×((y²)))+3⁴y⁴

((16×(x⁴))-((2³×3²×y²))+3⁴y⁴

(2⁴x⁴-(2³×3²x²y²))+3⁴y⁴

factoring 16⁴-72yx²y²+81y⁴

Try to factor this multi-variable trinomial using trail and error

Found a factorization:(4x²-9y²)×(4x²-9y²)

16x⁴-72x²y²+81y⁴ is. a perfect square

It factors into (4x²-9y²)×(4x²-9y²)

which is another way of writing (4x²-9y²)²

How to recognize a perfect square trinomial:

*It has three terms

*Two of its terms are perfect squares themselves

*The remaining term is twice the product of the square roots of the other two terms

Factoring:4x²-9y²

put the exponent aside,try to factor 4x²-9y²

Theory:A different of two perfect squares,A²-B² can be factored into (A+B)×(A-B)

Proof:(A+B)×(A-B)=

A²-AB+BA-B²=

A²-AB+AB-B²=

A²-B²

Note:AB=BA is the commutative property of multiplication.

Note:-AB+AB equals zero and I therefore eliminated from the expression.

Check:4 is the square of 2

Check:9 is the square of 3

Check:x² is the square of x¹

Check:y² is the square of y¹

Factorization is:(2x+3y)×(2x-3y)

Rais the exponent which was put aside

Factorization becomes:(2x+3y)²×(2x-3y)²

Final result (2x+3y)²×(2x-3y)²

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