1,a2-10a+25-y2-4yz-4z2
=(a−5)2-(y+2z)2
=(a−5−y−2z)(a−5+y+2z)
2.x2+3cd(2-3cd)-10xy-1+25y2
=x2+6cd−(3cd)2−10xy−1+(5y)2
=x2−10xy+(5y)2−(1−6cd+(3cd)2)
=(x−5y)2+6cd−1−(3cd)2
=(x−5y)2−(1−3cd)2
=(x−5y−1+3cd)(x−5y+1−3cd)
c: \(4b^2c^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc\right)^2-\left(b^2+c^2-a^2\right)^2\)
\(=\left(2bc+b^2+c^2-a^2\right)\left[2bc-b^2-c^2+a^2\right]\)
\(=\left[\left(b+c\right)^2-a^2\right]\left[a^2-\left(b-c\right)^2\right]\)
\(=\left(b+c+a\right)\left(b+c-a\right)\left(a-b+c\right)\left(a+b-c\right)\)
d: \(\left(4x^2-3x-18\right)^2-\left(4x^2+3x\right)^2\)
\(=\left(4x^2-3x-18+4x^2+3x\right)\left(4x^2-3x-18-4x^2-3x\right)\)
\(=\left(8x^2-18\right)\left(-6x-18\right)\)
\(=-6\cdot\left(x+3\right)\cdot2\left(4x^2-9\right)\)
\(=-12\left(x+3\right)\left(2x-3\right)\left(2x+3\right)\)
