Question

4(x-y)+x^2(y-2)+y^2(2-x) factories ​

Answer 1

Solution :

Now,

4 (x - y) + x²(y - 2) + y²(2 - x)

= 4 (x - y) + x²y - 2x² + 2y² - xy²

= 4 (x - y) + (x²y - xy²) - 2 (x² - y²)

= 4 (x - y) + xy (x - y) - 2 (x+ y) (x - y)

= (x - y) {4 + xy - 2 (x + y)}

= (x - y) (4 + xy - 2x - 2y) ,

which is the required factorization.

Method :

  To factorize any quadratic polynomial coming in middle term derivation, we have to write down the middle term as an operational value giving two terms.

E.g., x² + (a + b) x + ab

  = x² + ax + bx + ab

  = x (x + a) + b (x + a)

  = (x + a) (x + b)

Answer 2

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