Question

  

Answer 1

a: \(2x^2+5xy-3y^2\)

\(=2x^2+6xy-xy-3y^2\)

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

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

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

b: \(2a^2+3ab-5b^2\)

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

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

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

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

c: \(x^3+9x^2y+20xy^2\)

\(=x\cdot x^2+x\cdot9xy+x\cdot20y^2\)

\(=x\left(x^2+9xy+20y^2\right)\)

\(=x\left(x^2+4xy+5xy+20y^2\right)\)

\(=x\left[\left(x^2+4xy\right)+\left(5xy+20y^2\right)\right]\)

\(=x\left[x\left(x+4y\right)+5y\left(x+4y\right)\right]\)

\(=x\left(x+4y\right)\left(x+5y\right)\)