Answer :
To determine the simplest form of the given expression [tex]\((x + 7)(3x - 8)\)[/tex], we need to expand and simplify it step-by-step.
1. Distribute [tex]\(x\)[/tex] across [tex]\(3x - 8\)[/tex]:
[tex]\[ x \cdot (3x - 8) = 3x^2 - 8x \][/tex]
2. Distribute [tex]\(7\)[/tex] across [tex]\(3x - 8\)[/tex]:
[tex]\[ 7 \cdot (3x - 8) = 21x - 56 \][/tex]
3. Combine the results:
[tex]\[ (x \cdot 3x - x \cdot 8) + (7 \cdot 3x - 7 \cdot 8) = 3x^2 - 8x + 21x - 56 \][/tex]
4. Combine like terms [tex]\( -8x \)[/tex] and [tex]\( 21x \)[/tex]:
[tex]\[ 3x^2 + ( -8x + 21x) - 56 = 3x^2 + 13x - 56 \][/tex]
The simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex] is:
[tex]\[ 3x^2 + 13x - 56 \][/tex]
Thus, the correct answer is:
D. [tex]\(3 x^2 + 13 x - 56\)[/tex]
1. Distribute [tex]\(x\)[/tex] across [tex]\(3x - 8\)[/tex]:
[tex]\[ x \cdot (3x - 8) = 3x^2 - 8x \][/tex]
2. Distribute [tex]\(7\)[/tex] across [tex]\(3x - 8\)[/tex]:
[tex]\[ 7 \cdot (3x - 8) = 21x - 56 \][/tex]
3. Combine the results:
[tex]\[ (x \cdot 3x - x \cdot 8) + (7 \cdot 3x - 7 \cdot 8) = 3x^2 - 8x + 21x - 56 \][/tex]
4. Combine like terms [tex]\( -8x \)[/tex] and [tex]\( 21x \)[/tex]:
[tex]\[ 3x^2 + ( -8x + 21x) - 56 = 3x^2 + 13x - 56 \][/tex]
The simplest form of the expression [tex]\((x + 7)(3x - 8)\)[/tex] is:
[tex]\[ 3x^2 + 13x - 56 \][/tex]
Thus, the correct answer is:
D. [tex]\(3 x^2 + 13 x - 56\)[/tex]
