Question

Phân tích thành nhân tử ( phương pháp dùng hằng đẳng thức )

1) a² - 4b²

2) 4a² - b²

3) a² - 25

4) 25a² - \(\dfrac{1}{2}\)

5) x² + 10x + 25

Answer 1

\(1,a^2-4b^2=\left(a-2b\right)\left(a+2b\right)\)

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

\(3,a^2-25=\left(a-5\right)\left(a+5\right)\)

\(4,25a^2-\dfrac{1}{2}=\left(5a\right)^2-\left(\dfrac{1}{\sqrt{2}}\right)^2=\left(5a-\dfrac{1}{\sqrt{2}}\right)\left(5a+\dfrac{1}{\sqrt{2}}\right)\)

\(5,x^2+10x+25=x^2+2.x.5+5^2=\left(x+5\right)^2\)

Answer 2

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

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

3, \(a^2-25=a^2-5^2=\left(a-5\right)\left(a+5\right)\)

4, \(25a^2-\dfrac{1}{2}=\left(5a\right)^2-\sqrt{\left(\dfrac{1}{2}\right)^2}=\left(5a-\sqrt{\dfrac{1}{2}}\right)\left(5a+\sqrt{\dfrac{1}{2}}\right)\)

5, \(x^2+10x+25=x^2+2.x.5+5^2=\left(x+5\right)^2\)