Question

Written as a simplified polynomial in standard form, what is the result when left parenthesis, 3, x, minus, 2, right parenthesis, squared(3x−2)
2
is subtracted from 7, x, squared7x
2
?




Solve the problem just like the example below
⬇️
Written as a simplified polynomial in standard form, what is the result when
left parenthesis, 3, x, plus, 4, right parenthesis, squared
(3x+4)
2
is subtracted from
10
10?
Write as an expression:
Write as an expression:
10, minus, left parenthesis, 3, x, plus, 4, right parenthesis, squared
10−(3x+4)
2
10, minus, left parenthesis, 3, x, plus, 4, right parenthesis, left parenthesis, 3, x, plus, 4, right parenthesis
10−(3x+4)(3x+4)
10, minus, left parenthesis, 9, x, squared, plus, 12, x, plus, 12, x, plus, 16, right parenthesis
10−(9x
2
+12x+12x+16)
10, minus, left parenthesis, 9, x, squared, plus, 24, x, plus, 16, right parenthesis
10−(9x
2
+24x+16)
10, minus, 9, x, squared, minus, 24, x, minus, 16
10−9x
2
−24x−16
Final Answer:
Final Answer:
minus, 9, x, squared, minus, 24, x, minus, 6
−9x
2
−24x−6

Answer 1

To find the result of subtracting \((3x - 2)^2\) from \(7x^2\), we can follow the method you've specified.

1. Write as an expression:
\[
7x^2 - (3x - 2)^2
\]

2. Write as an expression:
\[
7x^2 - (3x - 2)(3x - 2)
\]

3. Expand \((3x - 2)(3x - 2)\):
\[
7x^2 - (9x^2 - 6x - 6x + 4)
\]

4. Combine like terms:
\[
7x^2 - (9x^2 - 12x + 4)
\]

5. Distribute the negative sign:
\[
7x^2 - 9x^2 + 12x - 4
\]

6. Combine like terms:
\[
(7x^2 - 9x^2) + 12x - 4
\]
\[
-2x^2 + 12x - 4
\]

Final Answer:
\[
-2x^2 + 12x - 4
\]