Question
Simplify(3x-4)(2x^2 minus 3X +5
Answers
GPT-4o mini
To simplify the expression \((3x - 4)(2x^2 - 3x + 5)\), you need to distribute each term in the first factor \((3x - 4)\) to every term in the second factor \((2x^2 - 3x + 5)\).
1. Distributing \(3x\) to each term in \((2x^2 - 3x + 5)\):
\[
3x \cdot 2x^2 = 6x^3
\]
\[
3x \cdot (-3x) = -9x^2
\]
\[
3x \cdot 5 = 15x
\]
So, the terms from this distribution are \(6x^3 - 9x^2 + 15x\).
2. Now, distributing \(-4\) to each term in \((2x^2 - 3x + 5)\):
\[
-4 \cdot 2x^2 = -8x^2
\]
\[
-4 \cdot (-3x) = 12x
\]
\[
-4 \cdot 5 = -20
\]
So, the terms from this distribution are \(-8x^2 + 12x - 20\).
3. Now, combine all the terms together:
\[
6x^3 + (-9x^2 - 8x^2) + (15x + 12x) - 20
\]
Combining like terms:
\[
6x^3 + (-17x^2) + (27x) - 20
\]
Thus, the simplified expression is:
\[
\boxed{6x^3 - 17x^2 + 27x - 20}
\]
1. Distributing \(3x\) to each term in \((2x^2 - 3x + 5)\):
\[
3x \cdot 2x^2 = 6x^3
\]
\[
3x \cdot (-3x) = -9x^2
\]
\[
3x \cdot 5 = 15x
\]
So, the terms from this distribution are \(6x^3 - 9x^2 + 15x\).
2. Now, distributing \(-4\) to each term in \((2x^2 - 3x + 5)\):
\[
-4 \cdot 2x^2 = -8x^2
\]
\[
-4 \cdot (-3x) = 12x
\]
\[
-4 \cdot 5 = -20
\]
So, the terms from this distribution are \(-8x^2 + 12x - 20\).
3. Now, combine all the terms together:
\[
6x^3 + (-9x^2 - 8x^2) + (15x + 12x) - 20
\]
Combining like terms:
\[
6x^3 + (-17x^2) + (27x) - 20
\]
Thus, the simplified expression is:
\[
\boxed{6x^3 - 17x^2 + 27x - 20}
\]