Solve (4+x^2)*(7+x^3)(11+x^5)(16+x^8)

$$( 4 + x ^ { 2 } ) \cdot ( 7 + x ^ { 3 } ) ( 11 + x ^ { 5 } ) ( 16 + x ^ { 8 } )$$

Evaluate

$$\left(x^{2}+4\right)\left(x^{3}+7\right)\left(x^{5}+11\right)\left(x^{8}+16\right)$$

Solution Steps

Use the distributive property to multiply 4+x^{2} by 7+x^{3}.

$$\left(28+4x^{3}+7x^{2}+x^{5}\right)\left(11+x^{5}\right)\left(16+x^{8}\right)$$

Use the distributive property to multiply 28+4x^{3}+7x^{2}+x^{5} by 11+x^{5} and combine like terms.

$$\left(308+39x^{5}+44x^{3}+4x^{8}+77x^{2}+7x^{7}+x^{10}\right)\left(16+x^{8}\right)$$

Use the distributive property to multiply 308+39x^{5}+44x^{3}+4x^{8}+77x^{2}+7x^{7}+x^{10} by 16+x^{8} and combine like terms.

$$4928+372x^{8}+624x^{5}+39x^{13}+704x^{3}+44x^{11}+4x^{16}+1232x^{2}+93x^{10}+112x^{7}+7x^{15}+x^{18}$$

Expand

$$x^{18}+4x^{16}+7x^{15}+39x^{13}+44x^{11}+93x^{10}+372x^{8}+112x^{7}+624x^{5}+704x^{3}+1232x^{2}+4928$$

Solution Steps

Use the distributive property to multiply 4+x^{2} by 7+x^{3}.

$$\left(28+4x^{3}+7x^{2}+x^{5}\right)\left(11+x^{5}\right)\left(16+x^{8}\right)$$

Use the distributive property to multiply 28+4x^{3}+7x^{2}+x^{5} by 11+x^{5} and combine like terms.

$$\left(308+39x^{5}+44x^{3}+4x^{8}+77x^{2}+7x^{7}+x^{10}\right)\left(16+x^{8}\right)$$

Use the distributive property to multiply 308+39x^{5}+44x^{3}+4x^{8}+77x^{2}+7x^{7}+x^{10} by 16+x^{8} and combine like terms.

$$4928+372x^{8}+624x^{5}+39x^{13}+704x^{3}+44x^{11}+4x^{16}+1232x^{2}+93x^{10}+112x^{7}+7x^{15}+x^{18}$$