Question

Answer 1

a) \(x^5+2x^3y+xy^2\\ =x\left(x^4+2x^2y+y^2\right)\\ =x\left(x^2+y\right)^2\)

b) \(14xy+49x^2-6y-9=\left(49x^2+14xy+y^2\right)-\left(y^2+6y+9\right)\\ =\left(7x+y\right)^2-\left(y+3\right)^2\\ =\left(7x+y-y-3\right)\left(7x+y+y+3\right)\\ =\left(7x-3\right)\left(7x+2y+3\right)\)

Answer 2

\(a,x^5+2x^3y+xy^2=x\left(x^4+2x^2y+y^2\right)=x\left(x^2+y\right)^2\\ b,14xy+49x^2-6y-9\\ =\left(49x^2+14xy+y^2\right)-\left(y^2+6y+9\right)\\ =\left(7x+y\right)^2-\left(y+3\right)^2\\ =\left(7x+y-y-3\right)\left(7x+y+y+3\right)\\ =\left(7x-3\right)\left(7x+2y+3\right)\)

Answer 3

b: \(49x^2+14xy-6y-9\)

\(=\left(7x-3\right)\left(7x+3\right)+2y\left(7x-3\right)\)

\(=\left(7x-3\right)\left(7x+3+2y\right)\)