Question

Chứng minh các đẳng thức:

a) (a + b)(a + b) = a² + 2ab + b²

b) (a - b)(a - b) = a² - 2ab + b²

c) (a - b)(a + b) = a² - b²

Answer 1

b) \(\left(a-b\right)\left(a-b\right)\)

\(=a\left(a+b\right)-b\left(a-b\right)\)

\(=a^2-ab-ba+b^2\)

\(=a^2-2ab+b^2\)

Answer 2

a) \(\left(a+b\right)\left(a+b\right)\)

\(=a\left(a+b\right)+b\left(a+b\right)\)

\(=a^2+ab+ba+b^2\)

\(=a^2+2ab+b^2\)

Answer 3

c) \(\left(a-b\right)\left(a+b\right)\)

\(=a\left(a+b\right)-b\left(a+b\right)\)

\(=a^2+ab-ba-b^2\)

\(=a^2-b^2\)