Question

Simplify (x^2+x) + n(x^2 + 4x) by distributing the n. Show that (x^2+x)+n(x^2 + 4x) is equivalent for n = 4 to (x^2 + x) + (x^2 + 4x) + (x^2 + 4x) + (x^2 + 4x)+(x^2 +4x). The simplified polynomial is .........The polynomials are equivalent since they both simplify to.........

Answer 1

ANSWERS

• The simplified polynomial is ,(1 + n)x² + (1 + 4n)x

,

• The polynomials are equivalent since they both simplify to ,5x² + 17x

EXPLANATION

For the first part we have to simplify the polynomial:

$(x^2+x)+n(x^2+4x)=x^2+x+nx^2+4nx$

This is the polynomial after distributing the n. Now we have to add like terms:

$=(1+n)x^2+(1+4n)x$

To show that one thing is equivalent to other thing we have to solve each side of the equality individually. If we get to the same result, then they are equivalent.

If we replace n = 4 into the expression above we have:

$(1+4)x^2+(1+4\cdot4)x=5x^2+(1+16)x=5x^2+17x$

Now we have to simplify the given expression:

$\begin{gathered} (x^2+x)+(x^2+4x)+(x^2+4x)+(x^2+4x)+(x^2+4x)= \\ \text{ adding like terms:} \\ =(1+1+1+1+1)x^2+(1+4+4+4+4)x \\ =5x^2+17x \end{gathered}$