Factorize each of the following algebraic expressions:
(1)`4x^2+12 x y+9y^2`
(2) `9a^2-24 a b+16 b^2`
(3)`p^2q^2-6p q r+9r^2`
(4) `36 a^2+36 a+9`

Explanation

(i) `4x^2+12 x y+9y^2`
Identity used:`(a+b)^2=a^2+2ab+b^2`
`=(2x)^2+2times2xtimes3y+(3y)^2`
`=(2x+3y)^2`
`=(2x+y)(2x+y)`

(ii) `9a^2-24 a b+16 b^2`
Identity used:`(a-b)^2=a^2-2ab+b^2`
`=(3a)^2-2times3atimes4b+(4b)^2`
`=(3a-4b)^2`
`=(3a-4b)(3a-4b)`

(iii) `p^2q^2-6p q r+9r^2`
Identity used:`(a-b)^2=a^2-2ab+b^2`
`=(pq)^2-2timespqtimes3r+(3r)^2`
`=(pq-3r)(pq-3r)`

(iv) `36a^2+36 a+9`
Identity used:`(a+b)^2=a^2+2ab+b^2`
`=(6a)^2+2times6atimes3+3^2`
`=(6a+3)(6a+3)`