Question

Factorise the following algebraic expression by using suitable identity x²y²-64​

Answer 1

GIVEN :-

• An algebric expression x²y² - 64.

TO FIND :-

• We have to factorise the given algebric expression.

SOLUTION :-

$\implies \displaystyle \sf \: x ^{2} y ^{2} - 64$

Here we have one law of exponent which can be used here i.e ( xy )¹ = x¹y¹.

$\implies \displaystyle \sf \:(xy) ^{2} - (8) ^{2}$

Now by using the algebric identity i.e (a + b)(a - b) = a² - b².

$\implies \displaystyle \sf \:(xy + 8)(xy - 8)$

Hence the factorised form of x²y² - 64 is (xy + 8)(xy - 8)

Answer 2

Answer:

Given :-

An algebraic expressions x² y² - 64

Identity to be used :-

(a² - b²) = (a + b)(a - b)

Solution :-

We will write

(xy)² - (8)²

• As 8² = 64

(xy + 8) (xy - 8)

Some more identity :-

(a + b)² = a² + b² + 2ab

(a - b)² = a² - 2ab + b²

(a + b)(a - b) = a² - b²