Answer :
To multiply the polynomials [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], you should follow these steps:
1. Distribute each term from the first polynomial to each term in the second polynomial.
Let's distribute each term:
- First, distribute [tex]\(4x^2\)[/tex] across every term in [tex]\(5x^2 - 3x\)[/tex]:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot -3x = -12x^3\)[/tex]
- Next, distribute [tex]\(7x\)[/tex] across every term in [tex]\(5x^2 - 3x\)[/tex]:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot -3x = -21x^2\)[/tex]
2. Combine all these products into a single expression:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
This gives us:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the result of the multiplication [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex] is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
The correct answer is option D: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. Distribute each term from the first polynomial to each term in the second polynomial.
Let's distribute each term:
- First, distribute [tex]\(4x^2\)[/tex] across every term in [tex]\(5x^2 - 3x\)[/tex]:
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot -3x = -12x^3\)[/tex]
- Next, distribute [tex]\(7x\)[/tex] across every term in [tex]\(5x^2 - 3x\)[/tex]:
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot -3x = -21x^2\)[/tex]
2. Combine all these products into a single expression:
[tex]\[
20x^4 - 12x^3 + 35x^3 - 21x^2
\][/tex]
3. Combine like terms:
- Combine the [tex]\(x^3\)[/tex] terms:
[tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
This gives us:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
So, the result of the multiplication [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex] is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
The correct answer is option D: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
