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Answer :
To solve the expression [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex], we can expand it using the distributive property, also known as the distributive law of multiplication over addition. Let's break it down step by step:
1. Distribute each term in the first binomial by each term in the second binomial.
- First, take [tex]\(4x^2\)[/tex] from the first binomial and distribute it:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex]
- Next, take [tex]\(7x\)[/tex] from the first binomial and distribute it:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times (-3x) = -21x^2\)[/tex]
2. Combine like terms:
- Terms with [tex]\(x^4\)[/tex]:
- [tex]\(20x^4\)[/tex] (there is no other [tex]\(x^4\)[/tex] term to combine with)
- Terms with [tex]\(x^3\)[/tex]:
- Combine [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
- Terms with [tex]\(x^2\)[/tex]:
- [tex]\(-21x^2\)[/tex] (there is no other [tex]\(x^2\)[/tex] term to combine with)
3. Write down the final expanded expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct answer is option B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
1. Distribute each term in the first binomial by each term in the second binomial.
- First, take [tex]\(4x^2\)[/tex] from the first binomial and distribute it:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex]
- Next, take [tex]\(7x\)[/tex] from the first binomial and distribute it:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times (-3x) = -21x^2\)[/tex]
2. Combine like terms:
- Terms with [tex]\(x^4\)[/tex]:
- [tex]\(20x^4\)[/tex] (there is no other [tex]\(x^4\)[/tex] term to combine with)
- Terms with [tex]\(x^3\)[/tex]:
- Combine [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex]
- Terms with [tex]\(x^2\)[/tex]:
- [tex]\(-21x^2\)[/tex] (there is no other [tex]\(x^2\)[/tex] term to combine with)
3. Write down the final expanded expression:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the correct answer is option B: [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
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