Question

Find the product of X²y², -6x³y⁴, x³y⁴

Answer 1

Answer:

This can be factored by completing the square.

Recall that perfect square trinomial x²+2xy+y² = (x+y)².

x⁴ + x²y² +y⁴ first term and 3rd term are perfect squares

= (x²)² + x²y² + (y²)² the middle term should to be 2x²y² to make it a perfect square, so add x²y² - x²y²

= (x²)² + x²y² + (y²)² + x²y² - x²y² combine 2nd and 4th terms

= (x²)² + 2 x²y² + (y²)² - x²y² first 3 terms form a perfect square trionomial

= (x² + y²)²- (xy)² it is a difference of two squares, now factor

=(x² + y² + xy)(x² + y² - xy)