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
(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.
I'm sorry I mistyped my answer. I said it was 21x+4. What is wrong with THIS answer? Thanks.
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 write down without calculation the expression
9x²+12x+4.
The answer you provided for the expression (3x+2)^2, which is 21x=4, is incorrect. It seems like you made some mistakes in simplifying the expression and equating it to a value. Let's break down how to correctly solve this expression.
To find the square of a binomial expression like (3x+2)^2, you need to apply the concept of expanding a binomial squared. This can be done using the FOIL method or by using the formula (a+b)^2 = a^2 + 2ab + b^2.
Applying this formula to (3x+2)^2, we get:
(3x+2)^2 = (3x)^2 + 2 * (3x) * (2) + (2)^2
= 9x^2 + 12x + 4.
Therefore, the correct simplified form of (3x+2)^2 is 9x^2 + 12x + 4.
It seems like you made mistakes in simplifying the expression and equating it to 21x=4, which is not an accurate representation of the expanded form of (3x+2)^2. Consequently, your answer was marked as partially correct, hence the minus one from your teacher.
To avoid similar mistakes in the future, remember to carefully apply the rules of algebra and take your time when simplifying expressions. Double-checking your work can also help catch any errors before submitting your answers.