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Simplify the following. 3((73)x2−25x+12)−7(x2+8x−16)3\left(\left(\frac{7}{3}\right)x^{2} - 25x + 12\right) - 7\left(x^{2} + 8x - 16\right)3((37​)x2−
Question

Simplify the following.
3((73)x225x+12)7(x2+8x16)3\left(\left(\frac{7}{3}\right)x^{2} - 25x + 12\right) - 7\left(x^{2} + 8x - 16\right)

A.

−131x + 148

B.

131x − 148

C.

131x + 148

D.

−131x − 148

Correct option is A

Given:3((73)x225x+12)7(x2+8x16)Formula Used:a(b+c+d)=ab+ac+adSolution:3(73x225x+12)7(x2+8x16)=(3×73x2)(3×25x)+(3×12)(7x2+56x112)=7x275x+367x256x+112=(7x27x2)+(75x56x)+(36+112)=131x+148\textbf{Given:} \\3\left(\left(\frac{7}{3}\right)x^{2} - 25x + 12\right) - 7\left(x^{2} + 8x - 16\right) \\\\\textbf{Formula Used:} \\a(b + c + d) = ab + ac + ad \\\\\textbf{Solution:} \\3\left(\frac{7}{3}x^{2} - 25x + 12\right) - 7\left(x^{2} + 8x - 16\right) \\= \left(3 \times \frac{7}{3}x^{2}\right) - (3 \times 25x) + (3 \times 12) \quad - \left(7x^{2} + 56x - 112\right) \\= 7x^{2} - 75x + 36 - 7x^{2} - 56x + 112 \\= (7x^{2} - 7x^{2}) + (-75x - 56x) + (36 + 112) \\= -131x + 148 \\​​

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