Solve (m^{7/2}-m^{2}+m^{3/2}-m+m^7/2-m^0)(m^7/2+m^0)=

$$( m ^ { 7 / 2 } - m ^ { 2 } + m ^ { 3 / 2 } - m + m ^ { 7 / 2 } - m ^ { 0 } ) ( m ^ { 7 / 2 } + m ^ { 0 } ) =$$

Evaluate

$$\left(m^{\frac{7}{2}}+1\right)\left(2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-1\right)$$

Solution Steps

Combine m^{\frac{7}{2}} and m^{\frac{7}{2}} to get 2m^{\frac{7}{2}}.

$$\left(2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-m^{0}\right)\left(m^{\frac{7}{2}}+m^{0}\right)$$

Calculate m to the power of 0 and get 1.

$$\left(2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-1\right)\left(m^{\frac{7}{2}}+m^{0}\right)$$

Calculate m to the power of 0 and get 1.

$$\left(2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-1\right)\left(m^{\frac{7}{2}}+1\right)$$

Use the distributive property to multiply 2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-1 by m^{\frac{7}{2}}+1 and combine like terms.

$$2\left(m^{\frac{7}{2}}\right)^{2}+m^{\frac{7}{2}}-m^{2}m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}m^{\frac{7}{2}}+m^{\frac{3}{2}}-mm^{\frac{7}{2}}-m-1$$

To raise a power to another power, multiply the exponents. Multiply \frac{7}{2} and 2 to get 7.

$$2m^{7}+m^{\frac{7}{2}}-m^{2}m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}m^{\frac{7}{2}}+m^{\frac{3}{2}}-mm^{\frac{7}{2}}-m-1$$

To multiply powers of the same base, add their exponents. Add 2 and \frac{7}{2} to get \frac{11}{2}.

$$2m^{7}+m^{\frac{7}{2}}-m^{\frac{11}{2}}-m^{2}+m^{\frac{3}{2}}m^{\frac{7}{2}}+m^{\frac{3}{2}}-mm^{\frac{7}{2}}-m-1$$

To multiply powers of the same base, add their exponents. Add \frac{3}{2} and \frac{7}{2} to get 5.

$$2m^{7}+m^{\frac{7}{2}}-m^{\frac{11}{2}}-m^{2}+m^{5}+m^{\frac{3}{2}}-mm^{\frac{7}{2}}-m-1$$

To multiply powers of the same base, add their exponents. Add 1 and \frac{7}{2} to get \frac{9}{2}.

$$2m^{7}+m^{\frac{7}{2}}-m^{\frac{11}{2}}-m^{2}+m^{5}+m^{\frac{3}{2}}-m^{\frac{9}{2}}-m-1$$

Factor

$$\left(m^{\frac{7}{2}}+1\right)\left(2m^{\frac{7}{2}}-m^{2}+m^{\frac{3}{2}}-m-1\right)$$