The product of the expression [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
What is an expression?
An expression is an algebraic term used for a mathematical statement that include variables and mathematical operations
Below is how to calculate the product
The product expression is given as:
[tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Express x^2 - 16 as a difference of two squares
[tex]\frac{(x - 4)(x + 4)}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Divide the expression
[tex]\frac{x - 4}{2} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex]
Factorize the other fraction
[tex]\frac{x - 4}{2} * \frac{x(x^2 - 2x + 1)}{(x -1)(x + 4)}[/tex]
Further factorize
[tex]\frac{x - 4}{2} * \frac{x(x- 1)(x - 1)}{(x -1)(x + 4)}[/tex]
Divide
[tex]\frac{x - 4}{2} * \frac{x(x- 1)}{x + 4}[/tex]
Multiply the fractions
[tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Hence, the product of [tex]\frac{x^2 - 16}{2x + 8} * \frac{x^3 - 2x^2 + x}{x^2 + 3x - 4}[/tex] is [tex]\frac{x(x- 1)(x - 4)}{x(x + 4)}[/tex]
Read more about algebraic expressions at:
https://brainly.com/question/4344214
