Question

1. $144x^{2}-25y^{2}$
2. $25u^{2}-v^{2}$
3. $121x^{2}-9y^{2}$
4. $49x^{2}-4y^{2}$
5. $81x^{2}-121y^{2}$
6. $36x^{2}-y^{2}$

Explanation:

Step1: Recognize difference of squares

Recall: $a^2 - b^2 = (a-b)(a+b)$

Step2: Factor 144x²−25y²

$144x^2=(12x)^2, 25y^2=(5y)^2$
$\implies 144x^2-25y^2=(12x-5y)(12x+5y)$

Step3: Factor 25u²−v²

$25u^2=(5u)^2, v^2=(v)^2$
$\implies 25u^2-v^2=(5u-v)(5u+v)$

Step4: Factor 121x²−9y²

$121x^2=(11x)^2, 9y^2=(3y)^2$
$\implies 121x^2-9y^2=(11x-3y)(11x+3y)$

Step5: Factor 49x²−4y²

$49x^2=(7x)^2, 4y^2=(2y)^2$
$\implies 49x^2-4y^2=(7x-2y)(7x+2y)$

Step6: Factor 81x²−121y²

$81x^2=(9x)^2, 121y^2=(11y)^2$
$\implies 81x^2-121y^2=(9x-11y)(9x+11y)$

Step7: Factor 36x²−y²

$36x^2=(6x)^2, y^2=(y)^2$
$\implies 36x^2-y^2=(6x-y)(6x+y)$

Answer:

1. $(12x-5y)(12x+5y)$
2. $(5u-v)(5u+v)$
3. $(11x-3y)(11x+3y)$
4. $(7x-2y)(7x+2y)$
5. $(9x-11y)(9x+11y)$
6. $(6x-y)(6x+y)$