a: \(=\left(3x+2\right)\left(9x^2-6x+4\right)\)
b: \(=a^2x^2+2axby+b^2y^2-a^2y^2-2abxy-b^2x^2\)
\(=x^2\left(a^2-b^2\right)-y^2\left(a^2-b^2\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(x-y\right)\left(x+y\right)\)
c: \(=4\left(x+3\right)-3x\left(x+3\right)\)
\(=\left(x+3\right)\left(4-3x\right)\)
a. \(27x^3+8\)
\(\Leftrightarrow\left(3x+2\right).\left(9x^2-6x+4\right)\)
b. \(\left(ax+by\right)^2-\left(ay+bx\right)^2\)
\(\Leftrightarrow\left(ax+by-ay-bx\right).\left(ax+by+ay+bx\right)\)
c. \(4.\left(x+3\right)-3x^2-9x\)
\(\Leftrightarrow4.\left(x+3\right)-3x.\left(x+3\right)\)
d. \(-16x^4y^2-24x^3y^3-9x^3y^2\)
\(\Leftrightarrow-x^3y^2.\left(16x+24y^2+9\right)\)
e. \(3x^2-3xy-5x+5y\)
\(\Leftrightarrow3x.\left(x-y\right)-5.\left(x-y\right)\)
\(\Leftrightarrow\left(x-y\right).\left(3x-5\right)\)
