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1, <=> \(\left(4x\right)^2-\left(9y\right)^2\)=\(\left(4x-9y\right)\left(4x+9y\right)\)
1) \(16x^2-81.y^2=\left(4x\right)^2-\left(9.y\right)^2=\left(4x-9y\right)\left(4x+9y\right)\)
2) \(\left(5x-3y\right)^2-\left(3x-5y\right)^2=\left(5x-3y-3x+5y\right)\left(5x-3y+3x-5y\right)=\left(2x+2y\right).\left(8x-8y\right)\)
\(=16.\left(x+y\right)\left(x-y\right)\)
3)\(4x^2-y^2+4y-4=4x^2-\left(y^2-4y+4\right)=\left(2x\right)^2-\left(y-2\right)^2=\left(2x-y+2\right).\left(2x+y-2\right)\)
4)\(9.\left(x-y\right)^2-16.\left(2x+y\right)^2=3^2.\left(x-y\right)^2-4^2.\left(2x+y\right)^2=\left(3x-3y\right)^2-\left(8x+4y\right)^2\)
\(=\left(3x-3y-8x-4y\right)\left(3x-3y+8x+4y\right)=\left(-5x-7y\right).\left(11x+y\right)\)
\(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x-y\right)^2-4\left(4x-y\right)\)
\(=\left(4x-y\right)\left(4x-y-4\right)\)
a) \(16x^2+y^2+4y-16x-8xy\)
\(=\left(4x\right)^2-8xy+y^2+4\left(y-4x\right)\)
\(=\left(4x-y\right)^2+4\left(y-4x\right)\)
\(=\left(y-4x\right)^2+4\left(y-4x\right)=\left(y-4x\right)\left(y-4x+4\right)\)
a) \(14\left(x-y\right)^2+21\left(y-x\right)\)
\(=14\left(x-y\right)^2-21\left(x-y\right)\)
\(=7\left(x-y\right)\left[2\left(x-y\right)-3\right]\)
\(=7\left(x-y\right)\left(2x-2y-3\right)\)
b) \(7x^5\left(y-3\right)-49x^4\left(3-y\right)^3\)
\(=7x^4\left(y-3\right)\left[x+7\left(y-3\right)^2\right]\)
\(=7x^4\left(y-3\right)\left(x+7y^2-42y+63\right)\)
c) \(\left(x^2-9\right)^2-x^2\left(x-3\right)^2\)
\(=\left(x-3\right)^2\left(x+3\right)^2-x^2\left(x-3\right)^2\)
\(=\left(x-3\right)^2\left[\left(x+3\right)^2-x^2\right]\)
\(=\left(x-3\right)^2\left(x^2+6x+9-x^2\right)\)
\(=3\left(x-3\right)^2\left(x+3\right)\)
d) \(\left(4x^2-1\right)^2-9\left(2x-1\right)^2\)
\(=\left(2x-1\right)^2\left(2x+1\right)^2-9\left(2x-1\right)^2\)
\(=\left(2x-1\right)^2\left[\left(2x+1\right)^2-9\right]\)
\(=\left(2x-1\right)^2\left(4x^2+4x+1-9\right)\)
\(=4\left(2x-1\right)^2\left(x^2+x-2\right)\)
\(=4\left(2x-1\right)^2\left(x-1\right)\left(x+2\right)\)