Solve 19*x^3*x^4+15*x*x^7-3left(5x^7+3{x}^8right)

$$19 \times { x }^{ 3 } \times { x }^{ 4 } +15 \times x \times { x }^{ 7 } -3 \left( 5 { x }^{ 7 } +3 { x }^{ 8 } \right)$$

Evaluate

$$2\left(3x+2\right)x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$19x^{7}+15xx^{7}-3\left(5x^{7}+3x^{8}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$19x^{7}+15x^{8}-3\left(5x^{7}+3x^{8}\right)$$

Use the distributive property to multiply -3 by 5x^{7}+3x^{8}.

$$19x^{7}+15x^{8}-15x^{7}-9x^{8}$$

Combine 19x^{7} and -15x^{7} to get 4x^{7}.

$$4x^{7}+15x^{8}-9x^{8}$$

Combine 15x^{8} and -9x^{8} to get 6x^{8}.

$$4x^{7}+6x^{8}$$

Expand

$$6x^{8}+4x^{7}$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 3 and 4 to get 7.

$$19x^{7}+15xx^{7}-3\left(5x^{7}+3x^{8}\right)$$

To multiply powers of the same base, add their exponents. Add 1 and 7 to get 8.

$$19x^{7}+15x^{8}-3\left(5x^{7}+3x^{8}\right)$$

Use the distributive property to multiply -3 by 5x^{7}+3x^{8}.

$$19x^{7}+15x^{8}-15x^{7}-9x^{8}$$

Combine 19x^{7} and -15x^{7} to get 4x^{7}.

$$4x^{7}+15x^{8}-9x^{8}$$

Combine 15x^{8} and -9x^{8} to get 6x^{8}.

$$4x^{7}+6x^{8}$$