Find the product of $5x^2+5xy-9y^2$ and $5x^2-5xy-9y^2$

Question

I did a straight-up multiplication of every term and got the correct answer, $25x^4-115x^2y^2+81y^4$

However given the identical expressions given (differing only in sign), I can't help but feel there is a pattern/simplification I'm not seeing here and a direct multiplication is in fact the wrong (or inefficient) method. I thought it could be of the form $(a+b)(a-b)$, but the signs don't match. Thank you.

perhaps this would be easier: Find the product of $5x^2-9y^2+5xy$ and $5x^2-9y^2-5xy$ — Will Jagy, Apr 05 '23 at 18:13

score 0 · Accepted Answer · answered Apr 04 '23 at 17:31

0

Let : $$a = 5x^2 -9y^2 \\ b = 5xy $$ This implies that $$5x^2 + 5xy -9y^2 = a + b $$ $$5x^2 - 5xy - 9y^2 = a - b $$

and therfore : $$(5x^2 + 5xy -9y^2)(5x^2 - 5xy - 9y^2)=(a-b)(a+b)=a^2-b^2 = (5x^2 -9y^2)^2 - (5xy)^2= 25x^4 + 81y^4-115x^2y^2$$

answered Apr 04 '23 at 17:31

Moustapha_M_I

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Find the product of $5x^2+5xy-9y^2$ and $5x^2-5xy-9y^2$

1 Answers1