How do you simplify #(5u ^ { 2} - 7u - 4) ( 2u ^ { 2} + 7u + 2#)?

2 Answers
George C.
Jan 27, 2017

#(5u^2-7u-4)(2u^2+7u+2) = 10u^4+21u^3-47u^2-42u-8#

Explanation:

For each power of #u# in descending order, pick out the combinations of one term from the first trinomial and one from the second such that their product will give that power of #u#. Add all of the matching products together:

#(5u^2-7u-4)(2u^2+7u+2)#

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

#= 10u^4+21u^3-47u^2-42u-8#

Jim G.
Jan 27, 2017

#10u^4+21u^3-47u^2-42u-8#

Explanation:

Each term in the second bracket must be multiplied by each term in the first bracket. This can be achieved as follows.

#(color(red)(5u^2-7u-4))(2u^2+7u+2)#

#=color(red)(5u^2)(2u^2+7u+2)color(red)(-7u)(2u^2+7u+2)color(red)(-4)(2u^2+7u+2)#

now distribute each set of brackets.

#=color(green)(10u^4+color(blue)(35u^3)+color(magenta)(10u^2)-color(blue)(14u^3)-color(magenta)(49u^2)-color(purple)(14u)#
#color(white)(x)-color(magenta)(8u^2)-color(purple)(28u)-color(brown)(8)#

collecting like terms.

#=10u^4+21u^3-47u^2-42u-8#

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