Question

CMR:A²-B²=(A+B).(A-B)

Answer 1

(a + b)(a - b)

= a(a + b) - b(a + b)

= a² + ab - ba - b²

= a² - b²

Answer 2

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

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

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

Answer 3

\(a^2+b^2\)

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

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

Answer 4

Ta có:

A²-B²=(A+B).(A-B)

          = A²+AB-BA-B²

          =A²-B²

Vậy A²-B²=(A-B).(A+B) (đfcm)

Answer 5

                            Giải

Ta có : \(\left(A+B\right)\left(A-B\right)\)

\(=A\left(A+B\right)-B\left(A+B\right)\)

\(=A^2+AB-AB-B^2\)

\(=A^2+0-B^2\)

\(=A^2-B^2\)

Vì \(A^2-B^2=A^2-B^2\)nên \(A^2-B^2=\left(A+B\right)\left(A-B\right)\left[đpcm\right]\)