Question

Factorise ax square - by square + bx square - at square

Answer 1

Your question needs a correction.

Correct question : ax² - by² + bx² - ay²


Now,

= > ax² - by² + bx² - ay²

= > ax² + bx² - by² - ay²

= > x²( a + b ) - y²( b + a )

= > ( a + b )( x² - y² )


From factorization, we know : -
( a² - b² ) = ( a + b )( a - b )


Thus,
= > ( a + b )( x - y )( x + y )


Therefore,
ax² - by² + bx² - ay² in factorized form is ( a + b )( x + y )( x - y ).

$\:$

Answer 2

ax²-by²+bx²-ay²

Taking variables that is positive sign together
and negative together

ax²+bx²-by²-ay²
Now taking common
x²(a+b)-y²(b+a)
x²(a+b)-y²(a+b)
(x²-y²)(a+b)

Using identity
a²-b²=>(a+b)(a-b)

(x²-y²)(a+b)
(x+y)(x-y)(a+b)


Hence answer is (x+y)(x-y)(a+b)