Answer :
Sure! Let's go through the process of multiplying the polynomials [tex]\((4x^2 + 7x)(5x^2 - 3x)\)[/tex] step by step.
When multiplying two binomials, we use the distributive property, multiplying each term in the first polynomial by each term in the second polynomial. Let's break it down:
1. Multiply the first term in the first polynomial ([tex]\(4x^2\)[/tex]) by each term in the second polynomial ([tex]\(5x^2\)[/tex] and [tex]\(-3x\)[/tex]):
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
2. Multiply the second term in the first polynomial ([tex]\(7x\)[/tex]) by each term in the second polynomial ([tex]\(5x^2\)[/tex] and [tex]\(-3x\)[/tex]):
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine all these results:
- The [tex]\(x^4\)[/tex] term: [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: [tex]\(-21x^2\)[/tex]
Putting it all together, we get the polynomial:
[tex]\[ 20x^4 + 23x^3 - 21x^2 \][/tex]
So the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
When multiplying two binomials, we use the distributive property, multiplying each term in the first polynomial by each term in the second polynomial. Let's break it down:
1. Multiply the first term in the first polynomial ([tex]\(4x^2\)[/tex]) by each term in the second polynomial ([tex]\(5x^2\)[/tex] and [tex]\(-3x\)[/tex]):
- [tex]\(4x^2 \cdot 5x^2 = 20x^4\)[/tex]
- [tex]\(4x^2 \cdot (-3x) = -12x^3\)[/tex]
2. Multiply the second term in the first polynomial ([tex]\(7x\)[/tex]) by each term in the second polynomial ([tex]\(5x^2\)[/tex] and [tex]\(-3x\)[/tex]):
- [tex]\(7x \cdot 5x^2 = 35x^3\)[/tex]
- [tex]\(7x \cdot (-3x) = -21x^2\)[/tex]
3. Combine all these results:
- The [tex]\(x^4\)[/tex] term: [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: [tex]\(-21x^2\)[/tex]
Putting it all together, we get the polynomial:
[tex]\[ 20x^4 + 23x^3 - 21x^2 \][/tex]
So the correct answer is B. [tex]\(20x^4 + 23x^3 - 21x^2\)[/tex].
