Solve 12s^2-14sq+18sq-21q^2

$$12 s ^ { 2 } - 14 s q + 18 s q - 21 q ^ { 2 }$$

Factor

$$\left(6s-7q\right)\left(3q+2s\right)$$

Solution Steps

Multiply and combine like terms.

$$-21q^{2}+4qs+12s^{2}$$

Consider -21q^{2}+4qs+12s^{2} as a polynomial over variable s.

$$12s^{2}+4qs-21q^{2}$$

Find one factor of the form ks^{m}+n, where ks^{m} divides the monomial with the highest power 12s^{2} and n divides the constant factor -21q^{2}. One such factor is 3q+2s. Factor the polynomial by dividing it by this factor.

$$\left(3q+2s\right)\left(-7q+6s\right)$$

Evaluate

$$\left(6s-7q\right)\left(3q+2s\right)$$

Solution Steps

Combine -14sq and 18sq to get 4sq.

$$12s^{2}+4sq-21q^{2}$$