Question

Bài 1: Phân tích đa thức thành nhân tử:

a) \(5x\left(x-10\right)-2x+2x+20\)

b) \(a\left(a-b\right)^2\left(a+b\right)-\left(b-a\right)^2\left(a^2-5ab+b^2\right)\)

c) \(\left(a-b\right)^{2-\left(b-a\right)\left(a-3b\right)}\)

Answer 1

\(5x.\left(x-10\right)-2x+2x+20\)

\(=5x^2-50x+20\)

\(=5\left(x^2-10x+5^2-21\right)\)

\(=5\left[\left(x-5\right)^2-\left(\sqrt{21}\right)^2\right]\)

\(=5\left(x-5-\sqrt{21}\right)\left(x-5+\sqrt{21}\right)\)

\(a\left(a-b\right)^2\left(a+b\right)-\left(b-a\right)^2\left(a^2-5ab+b^2\right)\)

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

\(=\left(a-b\right)^2\left[a.\left(a+b\right)-a^2+5ab-b^2\right]\)

\(=\left(a-b\right)^2\left[a^2+ab-a^2+5ab-b^2\right]\)

\(=\left(a-b\right)^2\left(6ab-b^2\right)\)

Sửa đề: \(\left(a-b\right)^2-\left(b-a\right)\left(a-3b\right)\)

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

\(=\left(a-b\right)\left(a-b+a-3b\right)\)

\(=\left(a-b\right)\left(2a-4b\right)\)

\(=2.\left(a-b\right)\left(a-2b\right)\)

Tham khảo nhé~