College

Multiply:

[tex]\left(4x^2 + 7x\right)\left(5x^2 - 3x\right)[/tex]

A. [tex]20x^4 + 23x^3 - 21x^2[/tex]
B. [tex]20x^4 + 23x^2 - 21x[/tex]
C. [tex]20x^4 + 35x^2 - 21x[/tex]
D. [tex]20x^4 + 35x^3 - 21x^2[/tex]

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].