How do you simplify #7a^ 3(6a^2 + a)^2- 4a ^ { 6}#?

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Answer 1 · 2018-04-20T03:03:55

#252a^7 + 80a^6 + 7a^5#

#7a^3(6a^2 + a)^2 - 4a^6#

First, simplify #(6a^2 + a)^2#:
#(6a^2 + a)(6a^2 + a)#

#36a^4 + 6a^3 + 6a^3 + a^2#

#36a^4 + 12a^3 + a^2#

Now put this back into the expression:
#7a^3(36a^4+12a^3+a^2) - 4a^6#

Expand:
#(7a^3 * 36a^4) + (7a^3 * 12a^3) + (7a^3 * a^2) - 4a^6#

When the bases are multiplied, then the powers are added:
#252a^(3+4) + 84a^(3+3) + 7a^(3+2) - 4a^6#

Simplify:
#252a^7 + 84a^6 + 7a^5 - 4a^6#

We know that #8a^6# and #-4a^6# are like terms (both have #a^6#) so we can combine them:
#252a^7 + 80a^6 + 7a^5#

Hope this helps!