Question

[Hoai Hoang]

Cho a²-b²=4C². CMR :

(5a-3b+8c) (5a-3b-8c)=(3a-5b)²

Answer 1

[Nhã Doanh]

\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(5a-3b\right)^2-\left(8c\right)^2\)

\(=25a^2-30ab+9b^2-16c^2\)

\(=25a^2-30ab+9b^2-16\left(a^2-b^2\right)\)

\(=25a^2-30ab+9b^2-16c^2+16b^2\)

\(=9a^2-30ab+25b^2\)

\(=\left(3a-5b\right)^2\)