Math

[Guest]

Factor:
(a-14bc³+d-1)²+(a+d-2)²(-196b²c⁶).

[shyamjayakannan]

[tex]\left(a-14bc^3+d-1\right)^2-196b^2c^6(a+d-2)^2=\left\{(a+d-2)+\left(1-14bc^3\right)\right\}^2-196b^2c^6(a+d-2)^2[/tex]
[tex]=(a+d-2)^2+2(a+d-2)\left(1-14bc^3\right)+\left(1-14bc^3\right)^2-196b^2c^6(a+d-2)^2[/tex]
[tex]=(a+d-2)^2\left(1-196b^2c^6\right)+2(a+d-2)\left(1-14bc^3\right)+\left(1-14bc^3\right)^2[/tex]
[tex]=\left(1-14bc^3\right)\left\{(a+d-2)^2\left(1+14bc^3\right)+2(a+d-2)+1-14bc^3\right\}[/tex]
[tex]=\left(1-14bc^3\right)\left[(a+d-2)\left\{(a+d-2)\left(1+14bc^3\right)+2\right\}+1-14bc^3\right][/tex]