Answer :
To multiply the polynomials
$$
(4x^2+7x)(5x^2-3x)
$$
we use the distributive property, multiplying each term in the first polynomial by each term in the second polynomial.
1. Multiply the first term of the first polynomial by each term of the second polynomial:
- $$4x^2 \cdot 5x^2 = 20x^4$$
- $$4x^2 \cdot (-3x) = -12x^3$$
2. Multiply the second term of the first polynomial by each term of the second polynomial:
- $$7x \cdot 5x^2 = 35x^3$$
- $$7x \cdot (-3x) = -21x^2$$
3. Now, combine the like terms. Notice that the terms in $$x^3$$ are like terms:
- $$-12x^3 + 35x^3 = 23x^3$$
So the polynomial becomes
$$
20x^4 + 23x^3 - 21x^2.
$$
Thus, the correct answer is
$$
\boxed{20x^4+23x^3-21x^2}.
$$
$$
(4x^2+7x)(5x^2-3x)
$$
we use the distributive property, multiplying each term in the first polynomial by each term in the second polynomial.
1. Multiply the first term of the first polynomial by each term of the second polynomial:
- $$4x^2 \cdot 5x^2 = 20x^4$$
- $$4x^2 \cdot (-3x) = -12x^3$$
2. Multiply the second term of the first polynomial by each term of the second polynomial:
- $$7x \cdot 5x^2 = 35x^3$$
- $$7x \cdot (-3x) = -21x^2$$
3. Now, combine the like terms. Notice that the terms in $$x^3$$ are like terms:
- $$-12x^3 + 35x^3 = 23x^3$$
So the polynomial becomes
$$
20x^4 + 23x^3 - 21x^2.
$$
Thus, the correct answer is
$$
\boxed{20x^4+23x^3-21x^2}.
$$
