Câu 1: Phân tích đa thức thành nhân tử
a) Ta có: \(x^3-x^2y+xy^2\)
\(=x\left(x^2-xy+y^2\right)\)
b) Ta có: \(5a\left(x-y\right)+2b\left(y-x\right)\)
\(=5a\left(x-y\right)-2b\left(x-y\right)\)
\(=\left(x-y\right)\left(5a-2b\right)\)
c) Ta có: \(x\left(x-y\right)-3x+3y\)
\(=x\left(x-y\right)-3\left(x-y\right)\)
\(=\left(x-y\right)\left(x-3\right)\)
d) Ta có: \(\left(x+1\right)\left(y-2\right)-\left(2-y\right)^2\)
\(=\left(x+1\right)\left(y-2\right)-\left(y-2\right)^2\)
\(=\left(y-2\right)\left(x+1-y+2\right)\)
\(=\left(y-2\right)\left(x-y+3\right)\)
e) Ta có: \(\left(3x-1\right)^2-16\)
\(=\left(3x-1\right)^2-4^2\)
\(=\left(3x-1-4\right)\left(3x-1+4\right)\)
\(=\left(3x-5\right)\left(3x+3\right)\)
\(=3\left(x+1\right)\left(3x-5\right)\)
f) Ta có: \(\left(5x-4\right)^2-49x^2\)
\(=\left(5x-4\right)^2-\left(7x\right)^2\)
\(=\left(5x-4-7x\right)\left(5x-4+7x\right)\)
\(=\left(-2x-4\right)\left(12x-4\right)\)
\(=-2\left(x+2\right)\cdot4\cdot\left(3x-1\right)\)
\(=-8\left(x+2\right)\left(3x-1\right)\)
g) Ta có: \(\left(2x+5\right)^2-\left(x-9\right)^2\)
\(=\left(2x+5-x+9\right)\left(2x+5+x-9\right)\)
\(=\left(x+14\right)\left(3x-4\right)\)
h) Ta có: \(9\left(2x+3\right)^2-4\left(x+1\right)^2\)
\(=\left(6x+9\right)^2-\left(2x+2\right)^2\)
\(=\left(6x+9-2x-2\right)\left(6x+9+2x+2\right)\)
\(=\left(4x+7\right)\left(8x+11\right)\)
Câu 3:
Ta có: \(7^{19}+7^{20}+7^{21}\)
\(=7^{19}\left(1+7+49\right)\)
\(=7^{19}\cdot57⋮57\)(đpcm)
