Answer :
To multiply the polynomials
[tex]$$\left(4x^2 + 7x\right)\left(5x^2 - 3x\right),$$[/tex]
we use the distributive property (also known as the FOIL method for binomials). Follow these steps:
1. Multiply the first term of the first polynomial by each term in the second polynomial:
[tex]$$4x^2 \cdot 5x^2 = 20x^4,$$[/tex]
[tex]$$4x^2 \cdot (-3x) = -12x^3.$$[/tex]
2. Multiply the second term of the first polynomial by each term in the second polynomial:
[tex]$$7x \cdot 5x^2 = 35x^3,$$[/tex]
[tex]$$7x \cdot (-3x) = -21x^2.$$[/tex]
3. Combine like terms (terms with the same power of [tex]$x$[/tex]):
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$-12x^3 + 35x^3 = 23x^3.$$[/tex]
Thus, the expanded expression is:
[tex]$$20x^4 + 23x^3 - 21x^2.$$[/tex]
Since this expression matches Option A, the correct answer is:
[tex]$$\boxed{20x^4 + 23x^3 - 21x^2}.$$[/tex]
[tex]$$\left(4x^2 + 7x\right)\left(5x^2 - 3x\right),$$[/tex]
we use the distributive property (also known as the FOIL method for binomials). Follow these steps:
1. Multiply the first term of the first polynomial by each term in the second polynomial:
[tex]$$4x^2 \cdot 5x^2 = 20x^4,$$[/tex]
[tex]$$4x^2 \cdot (-3x) = -12x^3.$$[/tex]
2. Multiply the second term of the first polynomial by each term in the second polynomial:
[tex]$$7x \cdot 5x^2 = 35x^3,$$[/tex]
[tex]$$7x \cdot (-3x) = -21x^2.$$[/tex]
3. Combine like terms (terms with the same power of [tex]$x$[/tex]):
- Combine the [tex]$x^3$[/tex] terms:
[tex]$$-12x^3 + 35x^3 = 23x^3.$$[/tex]
Thus, the expanded expression is:
[tex]$$20x^4 + 23x^3 - 21x^2.$$[/tex]
Since this expression matches Option A, the correct answer is:
[tex]$$\boxed{20x^4 + 23x^3 - 21x^2}.$$[/tex]
