Respuesta :
Answer:
[x(x - 1)(x - 4)]/(2(x + 4))
Step-by-step explanation:
We want to find;
[(x² - 16)/(2x + 8)] * [(x³ - 2x² + x)/(x² + 3x - 4)]
Now,
x² - 16 can be factorized as;
(x + 4)(x - 4)
Also, 2x + 8 can be factorized as;
2(x + 4)
Also, (x³ - 2x² + x) can factorized as;
x[x² - 2x + 1] = x[(x - 1)(x - 1)]
Also,(x² + 3x - 4) can be factorized out as; (x - 1)(x + 4)
So plugging in these factorized forms into the equation in the question, we have;
[(x + 4)(x - 4)/(2(x + 4))] * [x[(x - 1)(x - 1)] /((x - 1)(x + 4))
This gives;
((x - 4)/2) * x(x - 1)/(x +4)
This gives;
[x(x - 1)(x - 4)]/(2(x + 4))
The product of the given expression is [tex]\dfrac{x(x-1)(x-4)}{2(x+4)}[/tex] and this can be determined by using the factorization method.
Given :
[tex]\rm Expression \;\;- \;\; \dfrac{(x^2-16)}{(2x+8)}\times \dfrac{(x^3-2x^2+x)}{(x^2+3x-4)}[/tex]
The following calculation can be used to evaluate the given expression:
Step 1 - Write the given expression.
[tex]=\rm \dfrac{(x^2-16)}{(2x+8)}\times \dfrac{(x^3-2x^2+x)}{(x^2+3x-4)}[/tex]
Step 2 - Factorize the above equations.
[tex]=\dfrac{(x-4)(x+4)}{(2x+8)}\times \dfrac{x(x-1)^2}{(x^2+4x-x-4)}[/tex]
[tex]=\dfrac{(x-4)(x+4)}{(2x+8)}\times \dfrac{x(x-1)^2}{(x(x+4)-(x+4))}[/tex]
[tex]=\dfrac{(x-4)(x+4)}{(2x+8)}\times \dfrac{x(x-1)^2}{(x+4)(x-1)}[/tex]
Step 3 - Simplify the above expression.
[tex]=\dfrac{(x-4)}{2}\times \dfrac{x(x-1)}{(x+4)}[/tex]
Step 4 - Rewrite the above expression.
[tex]=\dfrac{x(x-1)(x-4)}{2(x+4)}[/tex]
So, the product of the given expression is [tex]\dfrac{x(x-1)(x-4)}{2(x+4)}[/tex] .
For more information, refer to the link given below:
https://brainly.com/question/21165491
