a) 3 x ( 4 x − 5 ) + 3 = 12 x 2 − 15 x + 3 when x=3 =12*3*3-15*3+3 =111-45 =66 b) a ( a 2 + a + 1 ) + 5 = a 3 + a 2 + a + 5 when a=0 =5 when a=1 =1+1+1+5 =8 when a=-1 = -1+1-1+5 =4.

Explanation

(i) `L.H.S. = (3x+7)^2 -84x = 9x^2+49+42x - 84x = 9x^2+49-42x`

` = (3x)^2+(7)^2 - 2**3x**7 = (3x-7)^2 = R.H.S.`



(ii)`L.H.S. = (9p-5q)^2+180pq = (9p)^2+(5q)^2-90pq+180pq`

`=(9p)^2+(5q)^2+90pq = (9p)^2+(5q)^2+2(9p)(5q) `

`= (9p+5q)^2 = R.H.S.`



(iii)`L.H.S. = (4/3m-3/4n)^2 +2mn= (4/3m)^2+(3/4n)^2 - 2**(4/3m)**(3/4n)+2mn`

...