Let's simplify the given expression step by step.
Given expression:
[tex]\[ 7x^2 - 6x(7 - 8x) \][/tex]
First, distribute [tex]\(-6x\)[/tex] through [tex]\( (7 - 8x) \)[/tex]:
[tex]\[
-6x \cdot 7 = -42x
\][/tex]
[tex]\[
-6x \cdot -8x = 48x^2
\][/tex]
Now, substitute these results back into the original expression:
[tex]\[
7x^2 - 42x + 48x^2
\][/tex]
Next, combine like terms:
[tex]\[
7x^2 + 48x^2 - 42x
\][/tex]
Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
(7 + 48)x^2 - 42x = 55x^2 - 42x
\][/tex]
The simplified expression is:
[tex]\[
55x^2 - 42x
\][/tex]
Now we can identify the coefficients for each term:
- For [tex]\(x^2\)[/tex]: [tex]\( 55 \)[/tex]
- For [tex]\(x\)[/tex]: [tex]\( -42 \)[/tex]
- For the constant term: [tex]\( 0 \)[/tex] (since there is no constant term in the simplified expression)
So, filling in the blanks:
- [tex]\( \text{For } x^2: \ 55 \)[/tex]
- [tex]\( \text{For } x: \ -42 \)[/tex]
- [tex]\( \text{For the constant term: } 0 \)[/tex]
This completes the simplification process.
