How do you multiply (2m+3)(m-1)(2m+3)(m−1)?

2 Answers
Fir3hawk
May 20, 2017

2m^2 +m -32m2+m−3

Explanation:

First of all, we use the FOIL method, which helps when distributing factored binomials.
F: Multiply first terms of each parenthesis
O: Multiply the outside terms (first term of the first parenthesis and
last term of the second parenthesis)
I: Multiply the inside terms (last term of the first parenthesis and first term of the second parenthesis)
L: Multiply last terms of each parenthesis

Now, to the math:

(2m+3)(m-1)(2m+3)(m−1)

F: (2m) * (m) = 2m^2(2m)⋅(m)=2m2

O: (2m)*(-1) = -2m(2m)⋅(−1)=−2m

I: (3)*(m) = 3m(3)⋅(m)=3m

L: (3)*(-1) = -3(3)⋅(−1)=−3

Now that we have all of our terms, we simplify to get the solution by adding like terms:

(2m^2) + (-2m) + (3m) + (-3)(2m2)+(−2m)+(3m)+(−3)
= 2m^2 + (3m-2m) -32m2+(3m−2m)−3
= 2m^2 +m -32m2+m−3

Jim G.
May 20, 2017

2m^2+m-32m2+m−3

Explanation:

Each term in the second bracket is multiplied by each term in the first bracket as shown below.

(color(red)(2m+3))(m-1)(2m+3)(m−1)

=color(red)(2m)(m-1)color(red)(+3)(m-1)=2m(m−1)+3(m−1)

=(color(red)(2m)xxm)+(color(red)(2m)xx-1)+(color(red)(3)xxm)+(color(red)(3)xx-1)=(2m×m)+(2m×−1)+(3×m)+(3×−1)

=2m^2+(-2m)+3m+(-3)=2m2+(−2m)+3m+(−3)

=2m^2-2m+3m-3=2m2−2m+3m−3

=2m^2+m-3=2m2+m−3

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