What is the product of #2x^2+7x-10# and #x+5# in standard form?

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Answer 1 · 2016-10-18T21:32:30

#2x^3 +17x^2+25x-50#

To begin, set up the expressions next to each other in parenthesis

#(x+5)(2x^2+7x-10)#

Now, you are going to distribute the first term in the first set of parenthesis throughout each term in the second set of parenthesis:

#(x+5)(2x^2+7x-10) =#

#=x(2x^2+7x-10) + 5(2x^2+7x-10)#

First, distribute #x# across #2x^2#, #7x#, and #-10#

So, multiply #x# by each of those terms to get:

#2x^3 +7x^2-10x#

Next, distribute the #5# throughout the set of parenthesis

#5(2x^2+7x-10)#

#=10x^2+35x-50#

Now add the 6 terms to get the final answer.

#2x^3 +7x^2-10x +10x^2+35x-50#

#=2x^3 +17x^2+25x-50#

Answer 2 · 2016-10-18T23:02:45

=#2x^3+17x^2+25x-50#

A Product is the answer to a multiplication operation.

We have two expressions to multiply together:

#(x+5)(2x^2+7x -10)#

Each term in the first bracket must be multiplied by each term in the second bracket .

This gives: #(color(red)(x)color(blue)(+5))(2x^2+7x -10)#

=#color(red)(2x^3+7x^2-10x)color(blue)( +10x^2+35x-50)#

There are now 6 terms. Add the like terms together.

=#2x^3+17x^2+25x-50#