what is the product?\n$\frac{x^{2}-16}{2x + 8}cdot\frac{x^{3}-2x^{2}+x}{x^{2}+3x - 4}$\n$\frac{x(x - 4)(x…

what is the product?\n$\frac{x^{2}-16}{2x + 8}cdot\frac{x^{3}-2x^{2}+x}{x^{2}+3x - 4}$\n$\frac{x(x - 4)(x - 1)}{2(x + 4)}$\n$\frac{x(x - 1)}{2}$\n$\frac{(x + 4)(x - 4)}{2x(x - 1)}$\n$\frac{(x - 4)(x - 1)}{2x(x + 4)}$

what is the product?\n$\frac{x^{2}-16}{2x + 8}cdot\frac{x^{3}-2x^{2}+x}{x^{2}+3x - 4}$\n$\frac{x(x - 4)(x - 1)}{2(x + 4)}$\n$\frac{x(x - 1)}{2}$\n$\frac{(x + 4)(x - 4)}{2x(x - 1)}$\n$\frac{(x - 4)(x - 1)}{2x(x + 4)}$

Answer

Explanation:

Step1: Factor the expressions

  • Factor (x^{2}-16) using the difference - of - squares formula (a^{2}-b^{2}=(a + b)(a - b)), so (x^{2}-16=(x + 4)(x - 4)).
  • Factor (2x + 8=2(x + 4)).
  • Factor (x^{3}-2x^{2}+x=x(x^{2}-2x + 1)=x(x - 1)^{2}) using the perfect - square formula (a^{2}-2ab + b^{2}=(a - b)^{2}).
  • Factor (x^{2}+3x - 4=(x + 4)(x - 1)) using the formula (x^{2}+(a + b)x+ab=(x + a)(x + b)) where (a = 4) and (b=-1). So the original expression (\frac{x^{2}-16}{2x + 8}\cdot\frac{x^{3}-2x^{2}+x}{x^{2}+3x - 4}=\frac{(x + 4)(x - 4)}{2(x + 4)}\cdot\frac{x(x - 1)^{2}}{(x + 4)(x - 1)}).

Step2: Simplify the product

Cancel out the common factors: Cancel out the common factor ((x + 4)) in the first fraction and ((x - 1)) in the second fraction. (\frac{(x + 4)(x - 4)}{2(x + 4)}\cdot\frac{x(x - 1)^{2}}{(x + 4)(x - 1)}=\frac{x(x - 4)(x - 1)}{2(x + 4)}).

Answer:

(\frac{x(x - 4)(x - 1)}{2(x + 4)})