Question
(3x^2-8)(4x^2+7)
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GPT-4o mini
To multiply the two polynomials \( (3x^2 - 8)(4x^2 + 7) \), we can use the distributive property (also known as the FOIL method for binomials). Here's how to do it step-by-step:
1. Distribute \( 3x^2 \) to both terms in the second polynomial:
\[
3x^2 \cdot 4x^2 + 3x^2 \cdot 7 = 12x^4 + 21x^2
\]
2. Distribute \( -8 \) to both terms in the second polynomial:
\[
-8 \cdot 4x^2 + (-8) \cdot 7 = -32x^2 - 56
\]
3. Now, combine all the terms:
\[
12x^4 + 21x^2 - 32x^2 - 56
\]
4. Combine the like terms:
\[
12x^4 + (21x^2 - 32x^2) - 56 = 12x^4 - 11x^2 - 56
\]
So the final result is:
\[
\boxed{12x^4 - 11x^2 - 56}
\]
1. Distribute \( 3x^2 \) to both terms in the second polynomial:
\[
3x^2 \cdot 4x^2 + 3x^2 \cdot 7 = 12x^4 + 21x^2
\]
2. Distribute \( -8 \) to both terms in the second polynomial:
\[
-8 \cdot 4x^2 + (-8) \cdot 7 = -32x^2 - 56
\]
3. Now, combine all the terms:
\[
12x^4 + 21x^2 - 32x^2 - 56
\]
4. Combine the like terms:
\[
12x^4 + (21x^2 - 32x^2) - 56 = 12x^4 - 11x^2 - 56
\]
So the final result is:
\[
\boxed{12x^4 - 11x^2 - 56}
\]
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