Solve b^2-by-72y^2

$$b ^ { 2 } - b y - 72 y ^ { 2 }$$

Factor

$$\left(b-9y\right)\left(8y+b\right)$$

Solution Steps

Consider b^{2}-by-72y^{2} as a polynomial over variable b.

$$b^{2}-yb-72y^{2}$$

Find one factor of the form b^{k}+m, where b^{k} divides the monomial with the highest power b^{2} and m divides the constant factor -72y^{2}. One such factor is -9y+b. Factor the polynomial by dividing it by this factor.

$$\left(-9y+b\right)\left(8y+b\right)$$

Evaluate

$$\left(b-9y\right)\left(8y+b\right)$$