a) \(40x^4-10x^2=10x^2\left(4x^2-1\right)=10x^2\left(2x-1\right)\left(2x+1\right)\)
b) \(16x^4-20x^2-y^2-5y=\left(4x^2-\dfrac{5}{2}\right)^2-\left(y-\dfrac{5}{2}\right)^2=\left(4x^2-\dfrac{5}{2}-y+\dfrac{5}{2}\right)\left(4x^2-\dfrac{5}{2}+y-\dfrac{5}{2}\right)=\left(4x^2-y\right)\left(4x^2+y-5\right)\)c)\(64a^2-9b^2-16a+1=\left(8a-1\right)^2-9b^2=\left(8a-1-3b\right)\left(8a-1+3b\right)\)d) \(5x^2+23x-10=5\left(x-\dfrac{2}{5}\right)\left(x+5\right)\)
a: \(40x^4-10x^2\)
\(=10x^2\left(4x^2-1\right)\)
\(=10x^2\cdot\left(2x-1\right)\left(2x+1\right)\)
b: \(16x^4-20x^2-y^2-5y\)
\(=\left(4x^2-y\right)\left(4x^2+y\right)-5\left(4x^2+y\right)\)
\(=\left(4x^2+y\right)\left(4x^2-y-5\right)\)
c: Ta có: \(64a^2-9b^2-16a+1\)
\(=\left(8a-1\right)^2-9b^2\)
\(=\left(8a-1-3b\right)\left(8a-1+3b\right)\)
d: Ta có: \(5x^2+23x-10\)
\(=5x^2+25x-2x-10\)
\(=\left(x+5\right)\left(5x-2\right)\)
e: Ta có: \(7x^2-13xy-2y^2\)
\(=7x^2-14xy+xy-2y^2\)
\(=7x\left(x-2y\right)+y\left(x-2y\right)\)
\(=\left(x-2y\right)\left(7x+y\right)\)
f: Ta có: \(x^4-23x^2y^2+y^4\)
\(=x^4+2x^2y^2+y^4-25x^2y^2\)
\(=\left(x^2+y^2-5xy\right)\left(x^2+y^2+5xy\right)\)
g: Ta có: \(\left(x^2+3x\right)^2+7\cdot\left(x^2+3x\right)+10\)
\(=\left(x^2+3x+2\right)\cdot\left(x^2+3x+5\right)\)
\(=\left(x+1\right)\left(x+2\right)\cdot\left(x^2+3x+5\right)\)
h: Ta có: \(x\left(x+1\right)\left(x+2\right)\left(x+3\right)-8\)
\(=\left(x^2+3x\right)\left(x^2+3x+2\right)-8\)
\(=\left(x^2+3x\right)^2+2\cdot\left(x^2+3x\right)-8\)
\(=\left(x^2+3x+4\right)\left(x^2+3x-2\right)\)
