Simplify (x2 + 7x + 12)(x2 + 3x + 5).
Mathematics · High School · Tue Nov 03 2020
Answered on
Given the numerical equation:
(x^2 + 7x + 12)(x^2 + 3x + 5)
Simplify.
Solution:
In order to Simplify the equation, we will use the FOIL Method.
Multiply the first term of the first equation, to the first, second and last term of the second equation. Then, multiply the second term of the first equation, to the first, second and last term of the second equation. Finally, multiply the last term of the first equation, to the first, second and last term of the second equation.
To clearly see how it works, here's a step by step solution.
= (x^2)(x^2)
=x^4
First term of the first equation multiplied to the first term of the second equation.
=(x^2)(3x)
= 3x^3
First term of the first equation multiplied to the second term of the second equation.
=(x^2)(5)
=-x^2
First term of the first equation multiplied to the last term of the second equation.
=(7x)(x^2)
=7x^3
Second term of the first equation multiplied to the first term of the second equation.
=(7x)(3x)
=21x^2
Second term of the first equation multiplied to the second term of the second equation.
=(7x)(5)
=35x
Second term of the first equation multiplied to the last term of the second equation.
=(12)(x^2)
=12x^2
Last term of the first equation multiplied to the first term of the second equation.
=(12)(3x)
=36x
Last term of the first equation multiplied to the second term of the second equation..
=(12)(5)
=60
Last term of the first equation multiplied to the last term of the second equation.
Put all the solutions back in one equation;
= x^4 +3x^3 +x^2 + 7x^3 + 21x^2 + 35x + 12x^2 + 36x + 60
Combine similar terms.
= x^4 +10x^3 +34x^2 + 71x + 60
Final answer: x^4 +10x^3 +34x^2 + 71x + 60