Find the HCF of the polynomials x⁴- y⁴and x²(x - y) + y² (x - y) + y - x
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Step-by-step explanation:
This can be factored by completing the square. Recall that perfect square trinomial x²+2xy+y?
= (x+y). x* + x°y° +y* first term and 3rd term are perfect squares
= (x³)² + x³y² + (y³)² the middle term %3D should to be 2xy? to make
it a perfect square, so add x*y? - x²y? = (x³)² + x°y² + (y³)² +x°y² - x²y² %3D combine 2nd and 4th terms
= (x)? + 2 x°y? + (y³)² - x³y² first 3 %3D terms form a perfect square trionomial = (x² + y²)²- (xy)² it is a difference of two squares, now factor =(x? + y² + xy)(x² + y² - xy)
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