Answer :
To find the product of the expression [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex], we can break it down into simple steps of multiplication.
1. Distribute [tex]\(2x^4\)[/tex] across each term inside the parentheses.
[tex]\[
2x^4 \times (4x^2 + 3x + 1) = (2x^4 \times 4x^2) + (2x^4 \times 3x) + (2x^4 \times 1)
\][/tex]
2. Multiply each pair of terms:
- For [tex]\(2x^4 \times 4x^2\)[/tex], multiply the coefficients (2 and 4) and add the exponents of like bases (x):
[tex]\[
2 \times 4 = 8 \quad \text{and} \quad x^4 \times x^2 = x^{4+2} = x^6
\][/tex]
So, [tex]\(2x^4 \times 4x^2 = 8x^6\)[/tex].
- For [tex]\(2x^4 \times 3x\)[/tex], multiply the coefficients (2 and 3) and add the exponents of like bases (x):
[tex]\[
2 \times 3 = 6 \quad \text{and} \quad x^4 \times x = x^{4+1} = x^5
\][/tex]
So, [tex]\(2x^4 \times 3x = 6x^5\)[/tex].
- For [tex]\(2x^4 \times 1\)[/tex], simply multiply the coefficient 2 by 1:
[tex]\[
2 \times 1 = 2
\][/tex]
So, [tex]\(2x^4 \times 1 = 2x^4\)[/tex].
3. Combine all the products:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]
Therefore, the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
1. Distribute [tex]\(2x^4\)[/tex] across each term inside the parentheses.
[tex]\[
2x^4 \times (4x^2 + 3x + 1) = (2x^4 \times 4x^2) + (2x^4 \times 3x) + (2x^4 \times 1)
\][/tex]
2. Multiply each pair of terms:
- For [tex]\(2x^4 \times 4x^2\)[/tex], multiply the coefficients (2 and 4) and add the exponents of like bases (x):
[tex]\[
2 \times 4 = 8 \quad \text{and} \quad x^4 \times x^2 = x^{4+2} = x^6
\][/tex]
So, [tex]\(2x^4 \times 4x^2 = 8x^6\)[/tex].
- For [tex]\(2x^4 \times 3x\)[/tex], multiply the coefficients (2 and 3) and add the exponents of like bases (x):
[tex]\[
2 \times 3 = 6 \quad \text{and} \quad x^4 \times x = x^{4+1} = x^5
\][/tex]
So, [tex]\(2x^4 \times 3x = 6x^5\)[/tex].
- For [tex]\(2x^4 \times 1\)[/tex], simply multiply the coefficient 2 by 1:
[tex]\[
2 \times 1 = 2
\][/tex]
So, [tex]\(2x^4 \times 1 = 2x^4\)[/tex].
3. Combine all the products:
[tex]\[
8x^6 + 6x^5 + 2x^4
\][/tex]
Therefore, the product of [tex]\(2x^4(4x^2 + 3x + 1)\)[/tex] is [tex]\(8x^6 + 6x^5 + 2x^4\)[/tex].
