a) 1 - 2y + y2
= (1-y)2
b) ( x + 1 )2 - 25
=( x + 1 )2 - 52
=(x+1+5)(x+1-5)
a) \(1-2y+y^2\)
\(=y^2-2\cdot y\cdot1+1^2\)
\(=\left(y-1\right)^2\)
b) \(\left(x+1\right)^2-25\)
\(=\left(x+1\right)^2-5^2\)
\(=\left(x+1-5\right)\left(x+1+5\right)\)
\(=\left(x-4\right)\left(x+6\right)\)
c) \(1-4x^2\)
\(=1^2-\left(2x\right)^2\)
\(=\left(1-2x\right)\left(1+2x\right)\)
d) \(8-27x^3\)
\(=2^3-\left(3x\right)^3\)
\(=\left(2-3x\right)\left(4+6x+9x^2\right)\)
e) \(27+27x+9x^2+x^3\)
\(=3^3+3\cdot3^2\cdot x+3\cdot3\cdot x^2+x^3\)
\(=\left(3+x\right)^3\)
f) \(8x^3-12x^2y+6xy^2-y^3\)
\(=\left(2x\right)^3-3\cdot\left(2x\right)^2\cdot y+3\cdot2x\cdot y^2-y^3\)
\(=\left(2x-y\right)^3\)
g) \(x^3+8y^3\)
\(=x^3+\left(2y\right)^3\)
\(=\left(x+2y\right)\left(x^2-2xy+4y^2\right)\)
a) 1 - 2y + y2
= (1-y)2
b) ( x + 1 )2 - 25
= (x+1)2 - 52 = (x+1-5)(x+1+5) = (x-4)(x+6)
c) 1 - 4x2
= 12 - (2x)2 = (1-2x)(1+2x)
d) 8 - 27x3
= 23 - (3x)3 = (2-3x)(4+6x+9x2)
e) 27 + 27x + 9x2+ x3
= (3+x)3
f) 8x3 - 12x2y + 6xy2- y3
= (2x-y)3
g) x3 + 8y3
= x3 + (2y)3 = (x+2y)(x2-2xy+4y2)
