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Answer :
To find the product of
[tex]$$2x^4 \left(2x^2 + 3x + 4\right),$$[/tex]
we will use the distributive property by multiplying [tex]$2x^4$[/tex] with each term inside the parentheses.
1. Multiply [tex]$2x^4$[/tex] by [tex]$2x^2$[/tex]:
- Multiply the coefficients: [tex]$2 \times 2 = 4$[/tex]
- Add the exponents for [tex]$x$[/tex]: [tex]$4 + 2 = 6$[/tex]
This gives the term:
[tex]$$4x^6.$$[/tex]
2. Multiply [tex]$2x^4$[/tex] by [tex]$3x$[/tex]:
- Multiply the coefficients: [tex]$2 \times 3 = 6$[/tex]
- Add the exponents for [tex]$x$[/tex]: [tex]$4 + 1 = 5$[/tex]
This gives the term:
[tex]$$6x^5.$$[/tex]
3. Multiply [tex]$2x^4$[/tex] by [tex]$4$[/tex]:
- Multiply the coefficients: [tex]$2 \times 4 = 8$[/tex]
- The exponent remains [tex]$4$[/tex] since [tex]$4$[/tex] is a constant.
This gives the term:
[tex]$$8x^4.$$[/tex]
Finally, we combine all the terms to obtain the final product:
[tex]$$4x^6 + 6x^5 + 8x^4.$$[/tex]
[tex]$$2x^4 \left(2x^2 + 3x + 4\right),$$[/tex]
we will use the distributive property by multiplying [tex]$2x^4$[/tex] with each term inside the parentheses.
1. Multiply [tex]$2x^4$[/tex] by [tex]$2x^2$[/tex]:
- Multiply the coefficients: [tex]$2 \times 2 = 4$[/tex]
- Add the exponents for [tex]$x$[/tex]: [tex]$4 + 2 = 6$[/tex]
This gives the term:
[tex]$$4x^6.$$[/tex]
2. Multiply [tex]$2x^4$[/tex] by [tex]$3x$[/tex]:
- Multiply the coefficients: [tex]$2 \times 3 = 6$[/tex]
- Add the exponents for [tex]$x$[/tex]: [tex]$4 + 1 = 5$[/tex]
This gives the term:
[tex]$$6x^5.$$[/tex]
3. Multiply [tex]$2x^4$[/tex] by [tex]$4$[/tex]:
- Multiply the coefficients: [tex]$2 \times 4 = 8$[/tex]
- The exponent remains [tex]$4$[/tex] since [tex]$4$[/tex] is a constant.
This gives the term:
[tex]$$8x^4.$$[/tex]
Finally, we combine all the terms to obtain the final product:
[tex]$$4x^6 + 6x^5 + 8x^4.$$[/tex]
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