Question

Factorize 2(x-y)²-9(x-y)+10​

Answer 1

Answer:

Step-by-step explanation:

2 (x + y)2 - 9(x + y) - 5

= 2 (x + y)2 - 10(x + y) + (x + y) - 5

= 2 (x + y) [(x + y) - 5] + 1 [(x + y) - 5]

= [2 (x + y) + 1] [(x + y) - 5]

Answer 2

$2(x-y)^2-9(x-y)+10=(x-y-2.5)(x-y-2)$

Step-by-step explanation:

Given : Expression $2(x-y)^2-9(x-y)+10$

To find : Factorize the expression ?

Solution :

Let $x-y=a$

The expression became, $2a^2-9a+10$

Applying quadratic formula,  $x=\frac{-b\pm\sqrt{b^2-4ac}}{2a}$

Here, a=2, b=-9 and c=10

$a=\frac{-(-9)\pm\sqrt{(-9)^2-4(2)(10)}}{2(2)}$

$a=\frac{9\pm\sqrt{1}}{4}$

$a=\frac{9\pm 1}{4}$

$a=\frac{9+ 1}{4},\frac{9-1}{4}$

$a=2.5,2$

The factor form is  $2a^2-9a+10=(a-2.5)(a-2)$

Substitute the value $x-y=a$,

$2(x-y)^2-9(x-y)+10=(x-y-2.5)(x-y-2)$

#Learn more

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