Question

Factorise :12(x²+7)²-8(x²+7)(2x-1)-15(2x-1)²

Answer 1

12(x²+7)²-8(x²+7)(2x-1)-15(2x-1)²

(x²+7)=a
(2x-1)=b

12a²-8ab-15b²=12a²-18ab+10ab-15b²=6a(2a-3b)+5b(2a-3b)=(2a-3b)(6a+5b)

[ 2(x²+7)-3(2x-1) ] [ 6(x²+7)+5(2x-1) ]=
( 2x²+14-6x+3 ) ( 6x²+42+10x-5) )=
(2x²-6x+17)(6x²+10x+37)=
2x²×6x² - 6x × 6x² +17×6x² + 2x²×10x - 6x ×10x+17×10x+2x²×37-6x ×37+17 × 37=
12x⁴ -36x³+102x²+20x³-60x²+170x+74x²-222x+629=
12x⁴ -36x³+20x³+102x²-60x²+74x²+170x-222x+629=
=12x⁴-16x³+116x²-52x+629

Answer 2

12(x^2+7)2−8(x^2+7)(2x−1)−15(2x−1)^2

Distribute:

=12x^4+168x^2+588+−16x^3+8x^2+−112x+56+−60x^2+60x+−15

Combine Like Terms:

=12x^4+168x^2+588+−16x^3+8x^2+−112x+56+−60x^2+60x+−15

=(12x^4)+(−16x^3)+(168x^2+8x^2+−60x^2)+(−112x+60x)+(588+56+−15)

=12x^4+−16x^3+116x^2+−52x+629