Solve 7w^2-3x^2+3wx+w^2-2x^2

$$7 w ^ { 2 } - 3 x ^ { 2 } + 3 w x + w ^ { 2 } - 2 x ^ { 2 }$$

Evaluate

$$\left(8w-5x\right)\left(x+w\right)$$

Solution Steps

Combine 7w^{2} and w^{2} to get 8w^{2}.

$$8w^{2}-3x^{2}+3wx-2x^{2}$$

Combine -3x^{2} and -2x^{2} to get -5x^{2}.

$$8w^{2}-5x^{2}+3wx$$

Factor

$$\left(8w-5x\right)\left(x+w\right)$$

Solution Steps

Multiply and combine like terms.

$$-5x^{2}+3wx+8w^{2}$$

Consider -5x^{2}+3wx+8w^{2} as a polynomial over variable w.

$$8w^{2}+3xw-5x^{2}$$

Find one factor of the form kw^{m}+n, where kw^{m} divides the monomial with the highest power 8w^{2} and n divides the constant factor -5x^{2}. One such factor is -5x+8w. Factor the polynomial by dividing it by this factor.

$$\left(-5x+8w\right)\left(x+w\right)$$