Answer :
Let's simplify the expression step-by-step:
The expression we need to simplify is:
[tex]\[ 4(3x - 2)(2x + 4) + 3x^2 + 5x - 6 \][/tex]
1. Expand the terms within the parentheses:
- First, expand [tex]\((3x - 2)(2x + 4)\)[/tex].
- Use the distributive property (FOIL method):
[tex]\[
(3x - 2)(2x + 4) = 3x(2x) + 3x(4) - 2(2x) - 2(4)
\][/tex]
[tex]\[
= 6x^2 + 12x - 4x - 8
\][/tex]
[tex]\[
= 6x^2 + 8x - 8
\][/tex]
2. Multiply by 4:
- Distribute 4 across the expression:
[tex]\[
4(6x^2 + 8x - 8) = 24x^2 + 32x - 32
\][/tex]
3. Combine all terms:
- Add the expanded result to the remaining terms in the original expression:
[tex]\[
24x^2 + 32x - 32 + 3x^2 + 5x - 6
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
24x^2 + 3x^2 = 27x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
32x + 5x = 37x
\][/tex]
- Combine the constant terms:
[tex]\[
-32 - 6 = -38
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[ 27x^2 + 37x - 38 \][/tex]
So, the simplified expression matches option H: [tex]\( 27x^2 + 37x - 38 \)[/tex].
The expression we need to simplify is:
[tex]\[ 4(3x - 2)(2x + 4) + 3x^2 + 5x - 6 \][/tex]
1. Expand the terms within the parentheses:
- First, expand [tex]\((3x - 2)(2x + 4)\)[/tex].
- Use the distributive property (FOIL method):
[tex]\[
(3x - 2)(2x + 4) = 3x(2x) + 3x(4) - 2(2x) - 2(4)
\][/tex]
[tex]\[
= 6x^2 + 12x - 4x - 8
\][/tex]
[tex]\[
= 6x^2 + 8x - 8
\][/tex]
2. Multiply by 4:
- Distribute 4 across the expression:
[tex]\[
4(6x^2 + 8x - 8) = 24x^2 + 32x - 32
\][/tex]
3. Combine all terms:
- Add the expanded result to the remaining terms in the original expression:
[tex]\[
24x^2 + 32x - 32 + 3x^2 + 5x - 6
\][/tex]
4. Combine like terms:
- Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
24x^2 + 3x^2 = 27x^2
\][/tex]
- Combine the [tex]\(x\)[/tex] terms:
[tex]\[
32x + 5x = 37x
\][/tex]
- Combine the constant terms:
[tex]\[
-32 - 6 = -38
\][/tex]
Putting it all together, the simplified expression is:
[tex]\[ 27x^2 + 37x - 38 \][/tex]
So, the simplified expression matches option H: [tex]\( 27x^2 + 37x - 38 \)[/tex].
