Question

a,4x^2-1 b, 25x^2-16y^2 c, x^2 y^2 -1 d, 4x^2-9(x-1)^2 d,25(x-3)^2-64(x+1)^2

Answer 1

a: \(4x^2-1=\left(2x\right)^2-1^2=\left(2x-1\right)\left(2x+1\right)\)

b: \(25x^2-16y^2=\left(5x\right)^2-\left(4y\right)^2\)

=(5x-4y)(5x+4y)

c: \(x^2y^2-1=\left(xy\right)^2-1^2=\left(xy-1\right)\cdot\left(xy+1\right)\)

d: \(4x^2-9\left(x-1\right)^2\)

\(=\left(2x\right)^2-\left(3x-3\right)^2\)

=(2x-3x+3)(2x+3x-3)

=(-x+3)(5x-3)

e: \(25\left(x-3\right)^2-64\left(x+1\right)^2\)

\(=\left(5x-15\right)^2-\left(8x+8\right)^2\)

\(=\left(5x-15-8x-8\right)\left(5x-15+8x+8\right)\)

\(=\left(-3x-23\right)\left(13x-7\right)\)