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Answer :
Certainly! Let's solve the multiplication problem step-by-step:
We need to multiply two expressions: [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex].
To do this, we will use the distributive property (also known as expansion and multiplication of polynomials).
1. Multiply the first term of the first expression by each term of the second expression:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex]
2. Multiply the second term of the first expression by each term of the second expression:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times (-3x) = -21x^2\)[/tex]
Now, we combine these results:
- The term with [tex]\(x^4\)[/tex] is [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- The term with [tex]\(x^2\)[/tex] is [tex]\(-21x^2\)[/tex].
So, the expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the answer is A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
We need to multiply two expressions: [tex]\((4x^2 + 7x)\)[/tex] and [tex]\((5x^2 - 3x)\)[/tex].
To do this, we will use the distributive property (also known as expansion and multiplication of polynomials).
1. Multiply the first term of the first expression by each term of the second expression:
- [tex]\(4x^2 \times 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \times (-3x) = -12x^3\)[/tex]
2. Multiply the second term of the first expression by each term of the second expression:
- [tex]\(7x \times 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \times (-3x) = -21x^2\)[/tex]
Now, we combine these results:
- The term with [tex]\(x^4\)[/tex] is [tex]\(20x^4\)[/tex].
- Combine the [tex]\(x^3\)[/tex] terms: [tex]\(-12x^3 + 35x^3 = 23x^3\)[/tex].
- The term with [tex]\(x^2\)[/tex] is [tex]\(-21x^2\)[/tex].
So, the expanded expression is:
[tex]\[
20x^4 + 23x^3 - 21x^2
\][/tex]
Therefore, the answer is A. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
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