Solve (a^3+b^3)+(a^2-b^2)

$$( a ^ { 3 } + b ^ { 3 } ) + ( a ^ { 2 } - b ^ { 2 } )$$

Factor

$$\left(a+b\right)\left(a^{2}-ab+a+b^{2}-b\right)$$

Solution Steps

Consider a^{3}+b^{3}+a^{2}-b^{2} as a polynomial over variable a.

$$a^{3}+a^{2}+b^{3}-b^{2}$$

Find one factor of the form a^{k}+m, where a^{k} divides the monomial with the highest power a^{3} and m divides the constant factor b^{3}-b^{2}. One such factor is a+b. Factor the polynomial by dividing it by this factor.

$$\left(a+b\right)\left(a^{2}-ab+a+b^{2}-b\right)$$

Evaluate

$$a^{3}+a^{2}+b^{3}-b^{2}$$