Question

phân tích các đa thức sau thành nhân tử:

(7x-4)^2-(2x+1)^2

49(y-4)^2-9(y+2)^2

8x^3+1/27

125-x^6

Answer 1

*\(\left(7x-4\right)^2-\left(2x+1\right)^2\)

\(=\left(7x-4-2x-1\right)\left(7x-4+2x+1\right)\)

\(=\left(5x-5\right)\left(9x-3\right)\)

*\(49\left(y-4\right)^2-9\left(y+2\right)^2\)

\(=7^2\left(y-4\right)^2-3^2\left(y+2\right)^2\)

\(=\left(7y-28\right)^2-\left(3y+6\right)^2\)

\(=\left(7y-28-3y-6\right)\left(7y-28+3y+6\right)\)

\(=\left(4y-34\right)\left(10y-22\right)\)

* \(8x^3+\dfrac{1}{27}=\left(2x\right)^3+\left(\dfrac{1}{3}\right)^3\)

\(=\left(2x+\dfrac{1}{3}\right)\left[\left(2x\right)^2-2x.\dfrac{1}{3}+\left(\dfrac{1}{3}\right)^2\right]\)

\(=\left(2x+\dfrac{1}{3}\right)\left(4x^2-\dfrac{2}{3}x+\dfrac{1}{9}\right)\)

\(125-x^6=5^3-\left(x^2\right)^3=\left(5-x^2\right)\left(25+5x^2+x^4\right)\)