Câu hỏi của Châu Hữu Phát

Question

Cho $a^2-b^2=4c^2$.Chứng minh rằng:$\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(3a-5b\right)^2$

Mr Lazy · Accepted Answer

$\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(5a-3b\right)^2-64c^2=25a^2-2.5.3ab+9b^2-16\left(a^2-b^2\right)$

$=9a^2-2.3.5ab+25b^2=\left(3a-5b\right)^2$

Câu trả lời:

$\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(5a-3b\right)^2-64c^2=25a^2-2.5.3ab+9b^2-16\left(a^2-b^2\right)$

$=9a^2-2.3.5ab+25b^2=\left(3a-5b\right)^2$