Answer :
Sure! Let's simplify the given expression step by step.
We start with the expression:
[tex]\[
\left(7x^6 - 2x^2 + 3x\right) - \left(8x^2 + 5x^6 - 4x\right)
\][/tex]
First, distribute the negative sign through the second set of parentheses:
[tex]\[
7x^6 - 2x^2 + 3x - 8x^2 - 5x^6 + 4x
\][/tex]
Next, combine like terms by grouping the terms with the same powers of [tex]\(x\)[/tex]:
1. Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
7x^6 - 5x^6 = 2x^6
\][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-2x^2 - 8x^2 = -10x^2
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
3x + 4x = 7x
\][/tex]
Now, putting it all together, we get:
[tex]\[
2x^6 - 10x^2 + 7x
\][/tex]
So, the simplified expression is:
[tex]\[
x \cdot (2x^5 - 10x + 7)
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
x \cdot (2x^5 - 10x + 7)
\][/tex]
We start with the expression:
[tex]\[
\left(7x^6 - 2x^2 + 3x\right) - \left(8x^2 + 5x^6 - 4x\right)
\][/tex]
First, distribute the negative sign through the second set of parentheses:
[tex]\[
7x^6 - 2x^2 + 3x - 8x^2 - 5x^6 + 4x
\][/tex]
Next, combine like terms by grouping the terms with the same powers of [tex]\(x\)[/tex]:
1. Combine the [tex]\(x^6\)[/tex] terms:
[tex]\[
7x^6 - 5x^6 = 2x^6
\][/tex]
2. Combine the [tex]\(x^2\)[/tex] terms:
[tex]\[
-2x^2 - 8x^2 = -10x^2
\][/tex]
3. Combine the [tex]\(x\)[/tex] terms:
[tex]\[
3x + 4x = 7x
\][/tex]
Now, putting it all together, we get:
[tex]\[
2x^6 - 10x^2 + 7x
\][/tex]
So, the simplified expression is:
[tex]\[
x \cdot (2x^5 - 10x + 7)
\][/tex]
Therefore, the simplified form of the given expression is:
[tex]\[
x \cdot (2x^5 - 10x + 7)
\][/tex]
