Question

Write as a product: ax*2+ay*2–bx*2–by*2+b–a

Answer 1

$ax^2 + ay^2 -bx^2 -by^2 + b - a = \left(x^2+y^2-1\right)\left(a-b\right)$

Solution:

Given that,

$ax^2 + ay^2 -bx^2 -by^2 + b - a$

We have to write the above expression as product

From given,

$ax^2 + ay^2 -bx^2 -by^2 + b - a$

$\mathrm{Factor\:out\:common\:term\:}a\\\\a\left(x^2+y^2-1\right)-bx^2-by^2+b\\\\\mathrm{Factor\:out\:common\:term\:}b\\\\a\left(x^2+y^2-1\right)+b\left(-x^2-y^2+1\right)\\\\\mathrm{Rewrite\:as}\\\\\left(x^2+y^2-1\right)a-\left(x^2+y^2-1\right)b\\\\\mathrm{Factor\:out\:common\:term\:}\left(x^2+y^2-1\right)\\\\\left(x^2+y^2-1\right)\left(a-b\right)$

Thus the given expression is written as product