a) x² - x - 56
b) x^4 + 64
c) 4x^4 + 81
d) x².+ 12x + 35
e) 5x² - x - 4
g) 4x^4 + 1
h) 64x^4 + y^4
a)\(x^2-x-56\)
\(=x^2-8x+7x-56\)
\(=\left(x^2-8x\right)+\left(7x-56\right)\)
\(=x\left(x-8\right)+7\left(x-8\right)\)
\(=\left(x-8\right)\left(x+7\right)\)
b)\(x^4+64\)
\(=\left(x^2\right)^2+8^2\)
\(=\left(x^2\right)^2+16x^2+8^2-16x^2\)
\(=\left(x^2+8\right)^2-\left(4x\right)^2\)
\(=\left(x^2+8-4x\right)\left(x^2+8+4x\right)\)
c)\(4x^4+81\)
\(=\left(2x^2\right)^2+9^2\)
\(=\left(2x^2\right)^2+36x^2+9^2-36x^2\)
\(=\left(2x^2+9\right)^2-\left(6x\right)^2\)
\(=\left(2x^2+9-6x\right)\left(2x^2+9+6x\right)\)
d)\(x^2+12x+35\)
\(=x^2+5x+7x+35\)
\(=\left(x^2+5x\right)+\left(7x+35\right)\)
\(=x\left(x+5\right)+7\left(x+5\right)\)
\(=\left(x+5\right)\left(x+7\right)\)
e)\(5x^2-x-4\)
\(=5x^2-5x+4x-4\)
\(=\left(5x^2-5x\right)+\left(4x-4\right)\)
\(=5x\left(x-1\right)+4\left(x-1\right)\)
\(=\left(x-1\right)\left(5x+4\right)\)
g)\(4x^4+1\)
\(=\left(2x^2\right)^2+1^2\)
\(=\left(2x^2\right)^2+4x^2+1^2-4x^2\)
\(=\left(2x^2+1\right)^2-4x^2\)
\(=\left(2x^2+1-4x\right)\left(2x^2+1+4x\right)\)
h)\(64x^4+y^4\)
\(=\left(8x^2\right)^2+\left(y^2\right)^2\)
\(=\left(8x^2\right)^2+16x^2y^2+\left(y^2\right)^2-16x^2y^2\)
\(=\left(8x^2+y^2\right)^2-\left(4xy\right)^2\)
\(=\left(8x^2+y^2-4xy\right)\left(8x^2+y^2+4xy\right)\)
