# Multiply: $(4 + x)(x^2 + 2x +3)$

How would I solve this: Multiply: $(4 + x)(x^2 + 2x +3)$

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How would you multiply $(a+b) \cdot c$ ? –  JavaMan Mar 14 '11 at 16:28
Distribute. Multiply. Add. –  Arturo Magidin Mar 14 '11 at 16:30

This question, as you probably know, requires the use of the distributive property. To use JavaMan's suggestion $$(a + b) \cdot c = a \cdot c + b \cdot c$$
Let "a + b" be your $4 + x$ and let "c" be your $x^2 + 2x + 3$

Then we need to multiply $a \cdot c$, or $4 \cdot (x^2 + 2x + 3)$, and add it to

$b \cdot c$, which is $x \cdot (x^2 + 2x + 3)$

So $$a\cdot c + b \cdot c = [4\cdot (x^2 + 2x +3)] + [x \cdot (x^2 + 2x + 3)]$$ After taking these steps, combine like terms and write the result in order of decreasing exponents (for convention's sake)

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First, distribute the 4. Add the products of 4 and $x^2$, 4 and 2x, 3 and 4.

Then, distribute the x. Add the products of x and $x^2$, x and 2x, 3 and x.

Then all you have to do is add all of the items you have left.

After the distributions, you should have

$4x^2 + 8x + 12 + x^3 + x^2 + 3x =$

$x^3 + 5x^2 +11x + 12$

(Yay cool text!)

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just put dollar signs around the parts you want to cool-ify. –  The Chaz 2.0 Mar 14 '11 at 18:16