a) \(\left(x^2-25\right)^2-\left(x-5\right)^2\)
\(=\left(x-5\right)^2\left(x+5\right)^2-\left(x-5\right)^2\)
\(=\left(x-5\right)^2\left[\left(x+5\right)^2-1\right]\)
\(=\left(x-5\right)^2\left(x^2+10x+25-1\right)\)
\(=\left(x-5\right)^2\left(x^2+10x+24\right)\)
b) \(\left(4x^2-25\right)^2-9\left(2x-5\right)^2\)
\(=\left(2x-5\right)^2\left(2x+5\right)^2-9\left(2x-5\right)^2\)
\(=\left(2x-5\right)^2\left[\left(2x+5\right)^2-9\right]\)
\(=\left(2x-5\right)^2\left(4x^2+20x+25-9\right)\)
\(=\left(2x-5\right)^2\left(4x^2+20x+16\right)\)
c) \(4\left(2x-3\right)^2-9\left(4x^2-9\right)^2\)
\(=4\left(2x-3\right)^2-9\left(2x-3\right)^2\left(2x+3\right)^2\)
\(=\left(2x-3\right)^2\left[4-9\left(2x+3\right)^2\right]\)
\(=\left(2x-3\right)^2\left[4-9\left(4x^2+12x+9\right)\right]\)
\(=\left(2x-3\right)^2\left(4-36x^2-108x-81\right)\)
\(=(2x-3)^2(-36x^2-108x-77)\)
d) \(a^6-a^4+2a^3+2a^2\)
\(=\left(a^6-a^4\right)+\left(2a^3+2a^2\right)\)
\(=a^4\left(a^2-1\right)+2a^2\left(a-1\right)\)
\(=a^4\left(a+1\right)\left(a-1\right)+2a^2\left(a-1\right)\)
\(=\left(a-1\right)\left[a^4\left(a+1\right)+2a^2\right]\)
\(=a^2\left(a-1\right)\left[a^2\left(a+1\right)+2\right]\)
\(=a^2\left(a-1\right)\left(a^3+a^2+2\right)\)
e) \(\left(3x^2+3x+2\right)^2-\left(3x^2+2x-2\right)^2\)
\(=\left[\left(3x^2+3x+2\right)-\left(3x^2+3x-2\right)\right]\left[\left(3x^2+3x+2\right)+\left(3x^2+3x-2\right)\right]\)
\(=\left(3x^2+3x+2-3x^2-3x+2\right)\left(3x^2+3x+2+3x^2+3x-2\right)\)
\(=4\left(6x^2+6x\right)\)
\(=4\cdot6x\left(x+1\right)\)
\(=24x\left(x+1\right)\)
a: =(x-5)^2*(x+5)^2-(x-5)^2
=(x-5)^2[(x+5)^2-1]
=(x-5)(x+5-1)(x+5+1)
=(x-5)(x+4)(x+6)
b: =(2x-5)^2*(2x+5)^2-9(2x-5)^2
=(2x-5)^2*[(2x+5)^2-9]
=(2x-5)^2*(2x+5-3)(2x+5+3)
=4(2x-5)^2*(x+1)(x+4)
c: =4(2x-3)^2-9*(2x-3)^2*(2x+3)^2
=(2x-3)^2*[4-9(2x+3)^2]
=(2x-3)^2*(2-6x-9)(2+6x+9)
=(2x-3)^2*(-7-6x)(11+6x)
d: =a^2(a^4-a^2+2a+2)
=a^2[a^4+2a^3+a^2-2a^3-4a^2-2a+2a^2+4a+2)
=a^2(a+1)^2*(a^2-2a+2)
f: =(3x^2+3x+2-3x^2-3x+2)(3x^2+3x+2+3x^2+3x-2)
=4(6x^2+6x)
=24x(x+1)
