Answer :
To solve the problem of finding the quadratic expression that represents the product of the factors [tex]\((2x+5)(7-4x)\)[/tex], we can use the distributive property or the FOIL method. Here’s how to do it step-by-step:
1. First (F): Multiply the first terms in each binomial.
[tex]\[ 2x \times 7 = 14x \][/tex]
2. Outer (O): Multiply the outer terms in the expression.
[tex]\[ 2x \times (-4x) = -8x^2 \][/tex]
3. Inner (I): Multiply the inner terms.
[tex]\[ 5 \times 7 = 35 \][/tex]
4. Last (L): Multiply the last terms in each binomial.
[tex]\[ 5 \times (-4x) = -20x \][/tex]
5. Combine all the products from the steps above to get the expanded expression:
[tex]\[ -8x^2 + 14x - 20x + 35 \][/tex]
6. Simplify by combining like terms:
[tex]\[ -8x^2 + (14x - 20x) + 35 \][/tex]
[tex]\[ -8x^2 - 6x + 35 \][/tex]
Therefore, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
This matches with option A:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
1. First (F): Multiply the first terms in each binomial.
[tex]\[ 2x \times 7 = 14x \][/tex]
2. Outer (O): Multiply the outer terms in the expression.
[tex]\[ 2x \times (-4x) = -8x^2 \][/tex]
3. Inner (I): Multiply the inner terms.
[tex]\[ 5 \times 7 = 35 \][/tex]
4. Last (L): Multiply the last terms in each binomial.
[tex]\[ 5 \times (-4x) = -20x \][/tex]
5. Combine all the products from the steps above to get the expanded expression:
[tex]\[ -8x^2 + 14x - 20x + 35 \][/tex]
6. Simplify by combining like terms:
[tex]\[ -8x^2 + (14x - 20x) + 35 \][/tex]
[tex]\[ -8x^2 - 6x + 35 \][/tex]
Therefore, the quadratic expression is:
[tex]\[ -8x^2 - 6x + 35 \][/tex]
This matches with option A:
A. [tex]\(-8x^2 - 6x + 35\)[/tex]
