(x^3 + 5)(2x – 1)(x^2 – 4)(x^2 + 4)
Mathematics · Middle School · Mon Jan 18 2021
Answered on
Given the numerical equation:
(x^3 + 5)(2x – 1)(x^2 – 4)(x^2 + 4)
Simplify.
Solution:
In order to simplify the given numerical equation, we simply need to apply the foil method, hence since we have 4 equations, we will FOIL by pair. Multiply the first term of the first equation, to the first and last term of the second equation. Then, multiply the last term of the first equation, to the first and last term of the second equation.
To clearly see how it works, here's a step by step solution.
1st and 2nd equation:
= (x^3)(2x)
= 2x^4
First term of the first equation multiplied to the first term of the second equation.
=(x^3)(-1)
= -x^3
First term of the first equation multiplied to the last term of the second equation.
=(5)(2x)
=10x
Last term of the first equation multiplied to the first term of the second equation.
=(5)(-1)
= -5
Last term of the first equation multiplied to the fast term of the second equation.
= 2x^4 - x^3 + 10x - 5
3rd and 4th equation:
= (x^2)(x^2)
= x^4
First term of the third equation multiplied to the first term of the fourth equation.
=(x^2)(4)
= 4x^2
First term of the third equation multiplied to the last term of the fourth equation.
=(-4)(x^2)
=-4x^2
Last term of the third equation multiplied to the first term of the fourth equation.
=(-4)(4)
= -16
Last term of the third equation multiplied to the fast term of the fourth equation.
= x^4 - 4x^2 + 4x^2 - 16
=x^4 - 16
Combine the two answers by FOILING
= (2x^4 - x^3 + 10x - 5)(x^4 - 16)
Follow the same step:
= (x^4)(2x^4)
=x^8
=(x^4)(-x^3)
=-x^7
=(x^4)(10x)
= 10x^5
=(x^4)(5)
=5x^4
=(-16)(2x^4)
=-3x^4
=(-16)(-x^3)
=16x^3
=(-16)(10x)
= -160x
=(-16)(-5)
= 180
=x^8 - x^7 + 10x^5 + 5x^4 - 3x^4 + 16x^3 - 160x + 180
=x^8 - x^7 + 10x^5 + 2x^4 + 16x^3 - 160x + 180
Final answer:
=x^8 - x^7 + 10x^5 + 2x^4 + 16x^3 - 160x + 180