# Simplify (3n^2+n+7)(5n^2-4n-1)

(3n2+n+7)(5n2-4n-1)
Expand (3n2+n+7)(5n2-4n-1) by multiplying each term in the first expression by each term in the second expression.
3n2(5n2)+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Simplify terms.
Simplify each term.
Rewrite using the commutative property of multiplication.
3⋅5(n2n2)+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n2 by n2 by adding the exponents.
Use the power rule aman=am+n to combine exponents.
3⋅5n2+2+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
3⋅5n4+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
3⋅5n4+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply 3 by 5.
15n4+3n2(-4n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Rewrite using the commutative property of multiplication.
15n4+3⋅-4(n2n)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n2 by n by adding the exponents.
Multiply n2 by n.
Raise n to the power of 1.
15n4+3⋅-4(n2n1)+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Use the power rule aman=am+n to combine exponents.
15n4+3⋅-4n2+1+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4+3⋅-4n2+1+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4+3⋅-4n3+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4+3⋅-4n3+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply 3 by -4.
15n4-12n3+3n2⋅-1+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply -1 by 3.
15n4-12n3-3n2+n(5n2)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Rewrite using the commutative property of multiplication.
15n4-12n3-3n2+5n⋅n2+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n by n2 by adding the exponents.
Move n2.
15n4-12n3-3n2+5(n2n)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n2 by n.
Raise n to the power of 1.
15n4-12n3-3n2+5(n2n1)+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Use the power rule aman=am+n to combine exponents.
15n4-12n3-3n2+5n2+1+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4-12n3-3n2+5n2+1+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4-12n3-3n2+5n3+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4-12n3-3n2+5n3+n(-4n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Rewrite using the commutative property of multiplication.
15n4-12n3-3n2+5n3-4n⋅n+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n by n by adding the exponents.
Move n.
15n4-12n3-3n2+5n3-4(n⋅n)+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Multiply n by n.
15n4-12n3-3n2+5n3-4n2+n⋅-1+7(5n2)+7(-4n)+7⋅-1
15n4-12n3-3n2+5n3-4n2+n⋅-1+7(5n2)+7(-4n)+7⋅-1
Move -1 to the left of n.
15n4-12n3-3n2+5n3-4n2-1⋅n+7(5n2)+7(-4n)+7⋅-1
Rewrite -1n as -n.
15n4-12n3-3n2+5n3-4n2-n+7(5n2)+7(-4n)+7⋅-1
Multiply 5 by 7.
15n4-12n3-3n2+5n3-4n2-n+35n2+7(-4n)+7⋅-1
Multiply -4 by 7.
15n4-12n3-3n2+5n3-4n2-n+35n2-28n+7⋅-1
Multiply 7 by -1.
15n4-12n3-3n2+5n3-4n2-n+35n2-28n-7
15n4-12n3-3n2+5n3-4n2-n+35n2-28n-7
15n4-7n3-3n2-4n2-n+35n2-28n-7
Subtract 4n2 from -3n2.
15n4-7n3-7n2-n+35n2-28n-7