How do you multiply #(- 4n ^ { 2} - 3n + 7) ( - 8n ^ { 2} - 5n - 2)#?

2 Answers
Mark D.
May 4, 2018

# 32n^4+44n^3-33n^2-29n-14#

Explanation:

Multiply all three terms in the second bracket by each of the three terms in the first bracket.

#(-4n^2-3n+7)(-8n^2-5n-2 )=#

# 32n^4+20n^3+8n^2+24n^3+15n^2+6n-56n^2-35n-14#

Now collect like terms

# 32n^4+44n^3-33n^2-29n-14#

Ridinion K.
May 4, 2018

#=32n^4+44n^3-33n^2-29n-14#

Explanation:

Step by step, multiply out the first term separately with each term in the second pair of brackets. Then take the second term in the first bracket and multiply out with each term in the second pair of brackets. Complete by doing the third term in the first bracket multiplied by each term of the second bracket. Complete by simplification:

#(-4n^2-3n+7)(-8n^2-5n-2)#:

#(-4n^2)*(-8n^2)=32n^4#

#(-4n^2)*(-5n)=20n^3#

#(-4n^2)*(-2)=8n^2#

Proceed to take second term of first bracket and multiply by each term in the second bracket:

#(-3n)*(-8n^2)=24n^3#

#(-3n)*(-5n)=15n^2#

#(-3n)*(-2)=6n#

Then take the last term in the first pair of brackets and multiply out with each term in the second pair of brackets:

#(7)*(-8n^2)=-56n^2#

#(7)*(-5n)=-35n#

#(7)*(-2)=-14#

Now write all terms that have been expanded together:

#=32n^4+20n^3+8n^2+24n^3+15n^2+6n-56n^2-35n-14#

Simplify:

#=32n^4+44n^3-33n^2-29n-14#

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