Question

giúp e với ạ

Answer 1

a)\(2x^2-7xy+5y^2\)

\(=2x^2-2xy-5xy+5y^2\)

\(=2x\left(x-y\right)-5y\left(x-y\right)\)

\(=\left(x-y\right)\left(2x-5y\right)\)

Answer 2

b)\(x^3+3x^2y-4xy^2-12y^3\)

\(=\left(x^3+3x^2y\right)-\left(4xy^2+12y^3\right)\)

\(=x^2\left(x+3y\right)-4y^2\left(x+3y\right)\)

\(=\left(x+3y\right)\left(x^2-4y^2\right)\)

\(=\left(x+3y\right)\left(x-2y\right)\left(x+2y\right)\)

Answer 3

\(\text{a) }A=2x^2-7xy+5y^2\\ =2x^2-2xy-5xy+5y^2\\ =\left(2x^2-2xy\right)-\left(5xy-5y^2\right)\\ =2x\left(x-y\right)-5y\left(x-y\right)\\ =\left(2x+5y\right)\left(x-y\right)\\ \)

\(\text{b) }B=x^3+3x^2y-4xy^2-12y^3\\ =\left(x^3+3x^2y\right)-\left(4xy^2+12y^3\right)\\ =x^2\left(x+3y\right)-4y^2\left(x+3y\right)\\ =\left(x^2-4y^2\right)\left(x+3y\right)\\ =\left(x+2y\right)\left(x-2y\right)\left(x+3y\right)\\ \)

\(\text{c) }C=x^3+4y^2-2xy+x^2+8y^3\\ =\left(x^3+8y^3\right)+\left(x^2-2xy+4y^2\right)\\ =\left(x+2y\right)\left(x^2-2xy+4y^2\right)+\left(x^2-2xy+4y^2\right)\\ =\left(x+2y+1\right)\left(x^2-2xy+4y^2\right)\)