High School

Multiply:

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

A. [tex]20x^4 + 35x^2 - 21x[/tex]

B. [tex]20x^4 + 23x^2 - 21x[/tex]

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

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

Answer :

Sure! Let's multiply the given polynomials step-by-step without relying on any code.

We have:

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

To multiply these, we'll use the distributive property (also known as FOIL for binomials), which involves multiplying each term in the first polynomial by each term in the second polynomial.

1. Multiply [tex]\(4x^2\)[/tex] with each term in [tex]\(5x^2 - 3x\)[/tex]:

- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]

2. Multiply [tex]\(7x\)[/tex] with each term in [tex]\(5x^2 - 3x\)[/tex]:

- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]

Now, combine all these results:

- [tex]\(20x^4\)[/tex] (from [tex]\(4x^2 \cdot 5x^2\)[/tex])
- [tex]\(-12x^3\)[/tex] (from [tex]\(4x^2 \cdot (-3x)\)[/tex])
- [tex]\(+35x^3\)[/tex] (from [tex]\(7x \cdot 5x^2\)[/tex])
- [tex]\(-21x^2\)[/tex] (from [tex]\(7x \cdot (-3x)\)[/tex])

Next, combine the like terms:

- [tex]\(20x^4\)[/tex]
- [tex]\((-12x^3 + 35x^3) = 23x^3\)[/tex]
- [tex]\(-21x^2\)[/tex]

Putting it all together, we have:

[tex]\[20x^4 + 23x^3 - 21x^2.\][/tex]

Therefore, the correct answer is:

D. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex]

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