Answer :
To solve the problem of multiplying [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], let's break it down step-by-step using the distributive property.
1. Multiply each term in the first expression by each term in the second expression:
- First term multiplication: [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex].
- Outer term multiplication: [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex].
- Inner term multiplication: [tex]\(7x \times 5x^2 = 35x^3\)[/tex].
- Last term multiplication: [tex]\(7x \times (-3x) = -21x^2\)[/tex].
2. Combine like terms:
- The [tex]\(x^4\)[/tex] term stays as it is: [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- The [tex]\(x^2\)[/tex] term stays as it is: [tex]\(-21x^2\)[/tex].
3. Write the final answer by putting it all together:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct option is B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. Multiply each term in the first expression by each term in the second expression:
- First term multiplication: [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex].
- Outer term multiplication: [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex].
- Inner term multiplication: [tex]\(7x \times 5x^2 = 35x^3\)[/tex].
- Last term multiplication: [tex]\(7x \times (-3x) = -21x^2\)[/tex].
2. Combine like terms:
- The [tex]\(x^4\)[/tex] term stays as it is: [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- The [tex]\(x^2\)[/tex] term stays as it is: [tex]\(-21x^2\)[/tex].
3. Write the final answer by putting it all together:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct option is B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
