Factorize each of the following expressions:
(1)`(3+2a)^2-25 a^2`
(2) `(x+y)^2-(a-b)^2`
(3)`1/(16)x^2y^24/(49)y^2z^2`
(4) `75 a^3b^3-108 a b^4`

Explanation

(i)`(3+2a)^2-25 a^2`
`=−21a^2+12a+9`
`=3(−7a−3)(a−1)`

(ii) `(x+y)^2-(a-b)^2`
`=(x+y+a-b)(x+y-a+b)`

(iii)`1/(16)x^2y^2-4/(49)y^2z^2`
`= (1/4xy)^2 – (2/7yz)^2 `
`= (xy/4 + 2yz/7) (xy/4 – 2yz/7)`
`= y2 (x/4 + 2/7z) (x/4 – 2/7z)`

(iv) `75 a^3b^3-108 a b^4`
`= 3ab^2 ( 25a^2 - 36b^2 )`
`= 3ab^2 [ ( 5a )^2 - ( 6b )^2 ]`
`= 3ab^2 ( 5a + 6b )( 5a - 6b )`