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Find the product of the given polynomials.

[tex]\[ (5x + 5 - 2x)(4 + 7x - 1) \][/tex]

A. [tex]\( 21x^2 + 24x + 15 \)[/tex]
B. [tex]\( 21x^2 + 15x + 44 \)[/tex]
C. [tex]\( 9x^2 + 35x + 15 \)[/tex]
D. [tex]\( 21x^2 + 44x + 15 \)[/tex]



Answer :

GinnyAnswer
To find the product of the given polynomials [tex]\( (5x + 5 - 2x)(4 + 7x - 1) \)[/tex], we should first combine like terms in each polynomial and then multiply the simplified forms. Here’s the step-by-step solution:

1. Simplify each polynomial:

[tex]\[ 5x + 5 - 2x = (5x - 2x) + 5 = 3x + 5 \][/tex]

[tex]\[ 4 + 7x - 1 = 7x + (4 - 1) = 7x + 3 \][/tex]

So, the given expression [tex]\( (5x + 5 - 2x)(4 + 7x - 1) \)[/tex] simplifies to [tex]\( (3x + 5)(7x + 3) \)[/tex].

2. Apply the distributive property (also known as the FOIL method for binomials) to multiply the polynomials:

[tex]\[ (3x + 5)(7x + 3) = 3x \cdot 7x + 3x \cdot 3 + 5 \cdot 7x + 5 \cdot 3 \][/tex]

3. Compute each product:

- [tex]\( 3x \cdot 7x = 21x^2 \)[/tex]
- [tex]\( 3x \cdot 3 = 9x \)[/tex]
- [tex]\( 5 \cdot 7x = 35x \)[/tex]
- [tex]\( 5 \cdot 3 = 15 \)[/tex]

4. Combine the results to form the polynomial expression:

[tex]\[ 21x^2 + 9x + 35x + 15 \][/tex]

5. Combine like terms (the [tex]\( x \)[/tex]-terms):

[tex]\[ 21x^2 + (9x + 35x) + 15 = 21x^2 + 44x + 15 \][/tex]

Thus, the product of the given polynomials [tex]\( (5x + 5 - 2x)(4 + 7x - 1) \)[/tex] simplifies to [tex]\( 21x^2 + 44x + 15 \)[/tex].

So, the correct answer is:

[tex]\[ \boxed{21x^2 + 44x + 15} \][/tex]

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