Question

Answer 1

a: \(5x^2y-10xy^2\)

\(=5xy\cdot x-5xy\cdot2y\)

=5xy(x-2y)

b: \(13x^4y^3-26x^2y^2z^2-39xy^2z^3\)

\(=13xy^2\cdot x^3y-13xy^2\cdot2xz^2-13xy^2\cdot3z^3\)

\(=13xy^2\left(x^3y-2xz^2-3z^3\right)\)

c: \(9x^2y^2+15x^2y-21xy^2\)

\(=3xy\cdot3xy+3xy\cdot5x-3xy\cdot7y\)

=3xy(3xy+5x-7y)

d: \(\frac12x\left(x^2-4\right)+4\left(x+2\right)\)

\(=\frac12x\left(x-2\right)\left(x+2\right)+4\left(x+2\right)\)

\(=\left(x+2\right)\left\lbrack\frac12x\left(x-2\right)+4\right\rbrack=\left(x+2\right)\left(\frac12x^2-x+4\right)\)