Question

1. $25m^2 - 9$
2. $16v^2 - 9$
3. $y^2 - x^2$
4. $121y^2 - 36x^2$
5. $9u^2 - 4v^2$
6. $64a^2 - 25b^2$

Explanation:

Step1: Recognize difference of squares

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

Step2: Factor $25m^2 -9$

$25m^2=(5m)^2$, $9=3^2$, so:
$25m^2 -9=(5m-3)(5m+3)$

Step3: Factor $16v^2 -9$

$16v^2=(4v)^2$, $9=3^2$, so:
$16v^2 -9=(4v-3)(4v+3)$

Step4: Factor $y^2 -x^2$

$y^2=(y)^2$, $x^2=(x)^2$, so:
$y^2 -x^2=(y-x)(y+x)$

Step5: Factor $121y^2 -36x^2$

$121y^2=(11y)^2$, $36x^2=(6x)^2$, so:
$121y^2 -36x^2=(11y-6x)(11y+6x)$

Step6: Factor $9u^2 -4v^2$

$9u^2=(3u)^2$, $4v^2=(2v)^2$, so:
$9u^2 -4v^2=(3u-2v)(3u+2v)$

Step7: Factor $64a^2 -25b^2$

$64a^2=(8a)^2$, $25b^2=(5b)^2$, so:
$64a^2 -25b^2=(8a-5b)(8a+5b)$

Answer:

1. $(5m-3)(5m+3)$
2. $(4v-3)(4v+3)$
3. $(y-x)(y+x)$
4. $(11y-6x)(11y+6x)$
5. $(3u-2v)(3u+2v)$
6. $(8a-5b)(8a+5b)$