Asked by Amelie

On my quiz for (3x+2)^2, I wrote the answer as 21x=4. My teacher gave me a minus one, which meant it was half wrong. What is wrong about my answer? Thanks
Answered by MathMate
(3x+2)^2 is an expression,
21x=4 is an equation.
As far as I know, they have nothing to do with one another. Your teacher must be a generous one.
The expression could be expanded to
9x²+12x+4, but I do not know if this is what the instructions require.
Answered by Amelie
I'm sorry I mistyped my answer. I said it was 21x+4. What is wrong with THIS answer? Thanks.
Answered by MathMate
When you have two terms in x that multiply together, you would expect a term in x² which is missing from your answer.

Your teacher IS generous, because he/she believes that you have added the coefficients 9 and 12 together to make 21.
(c.f. correct answer of 9x²+12x+4).

What you would do in a case like this is to use the FOIL rule after writing the expression as
(3x+2)(3x+2)
3x*3x=9x²
3x*2=6x
2*3x=6x
2*2=4
for a total of 9x²+12x+4

If you are familiar with squaring of binomial expressions, you could use the following identity:
(ax+b)²
=a²x²+2abx+b²
Since a=3, b=2,
you can <i>write down</i> without calculation the expression
9x²+12x+4.
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