Giải toán 8 tập 1: Câu 43 sgk trang 20

a) \(x^2 + 6x + 9\)
\(= x^2 + 2.x.3 + 3^2\)
\(= (x + 3)^2\)
b) \(10x - 25 - x^2\)
\(= -(-10x + 25 + x^2)\)
\(= -(25 -10x + x^2)\)
\(= -(5^2 - 2.5.x + x^2)\)
\(= -(5 - x)^2\)
c) \(8x^3 - \dfrac{1}{8}\)
\(= (2x)^3 - \left(\dfrac{1}{2}\right)^3\)
\(= \left(2x - \dfrac{1}{2}\right) \left[(2x)^2 + 2.x.\dfrac{1}{2} +\left(\dfrac{1}{2}\right)^2 \right]\)
\(= \left(2x - \dfrac{1}{2}\right)\left(4x^2 + x+\dfrac{1}{4} \right)\)
d) \(\dfrac{1}{25}x^2 - 64y^2 \)
\(= \left(\dfrac{1}{5}x\right)^2 - (8y)^2\)
\(= \left(\dfrac{1}{5}x - 8y\right)\left(\dfrac{1}{5}x + 8y\right)\)