Question

Viết các biểu thức sau dưới dạng tích

a) x^2 -6x +9

b) x^2 +x +1/4

c) 4x^2 -1/16

d) (a+b)^2 -4

e) (a^2 +9)^2 -36a^2

Answer 1

a) \(x^2-6x+9=\left(x-3\right)^2\)

b) \(x^2+x+\frac{1}{4}=\left(x+\frac{1}{2}\right)^2\)

c) \(4x^2-\frac{1}{16}=\left(2x-\frac{1}{4}\right)\left(2x+\frac{1}{4}\right)\)

d) \(\left(a+b\right)^2-4=\left(a+b-2\right)\left(a+b+2\right)\)

e) \(\left(a^2+9\right)^2-36a^2=\left(a^2-6a+9\right)\left(a^2+6a+9\right)\)

\(=\left(a-3\right)^2\cdot\left(a+3\right)^2\)