+0

# help poly

0
240
1
+814

Let $$f(x)=x+5$$ and let $$g(x)=x^2+1$$. Let  $$p(x)=g(x)+f(x)$$and let $$q(x)=g(x)-f(x)$$. Find $$p(x)\cdot q(x)$$.

Aug 1, 2018

#1
+22861
+2

Let
$$f(x)=x+5$$
and let
$$g(x)=x^2+1$$.
Let
$$p(x)=g(x)+f(x)$$
and let
$$q(x)=g(x)-f(x)$$.
Find
$$p(x)\cdot q(x)$$.

$$\begin{array}{|rcll|} \hline p(x)\cdot q(x) &=& \Big( g(x)+f(x) \Big) \Big( g(x)-f(x) \Big) \\ &=& [g(x)]^2-[f(x)]^2 \\ &=& (x^2+1)^2-(x+5)^2 \\ &=& x^4+2x^2+1 -(x^2+10x+25) \\ &=& x^4+2x^2+1 -x^2-10x-25 \\ &\mathbf{=}& \mathbf{x^4+x^2-10x-24} \\ \hline \end{array}$$

Aug 1, 2018

#1
+22861
+2

Let
$$f(x)=x+5$$
and let
$$g(x)=x^2+1$$.
Let
$$p(x)=g(x)+f(x)$$
and let
$$q(x)=g(x)-f(x)$$.
Find
$$p(x)\cdot q(x)$$.

$$\begin{array}{|rcll|} \hline p(x)\cdot q(x) &=& \Big( g(x)+f(x) \Big) \Big( g(x)-f(x) \Big) \\ &=& [g(x)]^2-[f(x)]^2 \\ &=& (x^2+1)^2-(x+5)^2 \\ &=& x^4+2x^2+1 -(x^2+10x+25) \\ &=& x^4+2x^2+1 -x^2-10x-25 \\ &\mathbf{=}& \mathbf{x^4+x^2-10x-24} \\ \hline \end{array}$$

heureka Aug 1, 2018