(2v+1)(8v2+4v-7)

Expand (2v+1)(8v2+4v-7) by multiplying each term in the first expression by each term in the second expression.

2v(8v2)+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Simplify each term.

Rewrite using the commutative property of multiplication.

2⋅8(v⋅v2)+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Multiply v by v2 by adding the exponents.

Multiply v by v2.

Raise v to the power of 1.

2⋅8(v1v2)+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Use the power rule aman=am+n to combine exponents.

2⋅8v1+2+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

2⋅8v1+2+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Add 1 and 2.

2⋅8v3+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

2⋅8v3+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Multiply 2 by 8.

16v3+2v(4v)+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Multiply v by v.

16v3+2⋅4v2+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Multiply 2 by 4.

16v3+8v2+2v⋅-7+1(8v2)+1(4v)+1⋅-7

Multiply -7 by 2.

16v3+8v2-14v+1(8v2)+1(4v)+1⋅-7

Multiply 8v2 by 1.

16v3+8v2-14v+8v2+1(4v)+1⋅-7

Multiply 4v by 1.

16v3+8v2-14v+8v2+4v+1⋅-7

Multiply -7 by 1.

16v3+8v2-14v+8v2+4v-7

16v3+8v2-14v+8v2+4v-7

Simplify by adding terms.

Add 8v2 and 8v2.

16v3+16v2-14v+4v-7

Add -14v and 4v.

16v3+16v2-10v-7

16v3+16v2-10v-7

16v3+16v2-10v-7

Simplify (2v+1)(8v^2+4v-7)