How would I solve this: Multiply: $(4 + x)(x^2 + 2x +3)$
Multiply: $(4 + x)(x^2 + 2x +3)$
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4Distribute. Multiply. Add. – 2011-03-14
2 Answers
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)
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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4just put dollar sig$n$s around the parts you want to cool-ify. – 2011-03-14