If 5(3x + 4) - 8(6x + 7) = 9x - 8, then what is the value of (x2 - 2x + 1) ?

Concept: For any values a and b, (a − b)2 = a2 − 2ab + b2. The expression x2 − 2x + 1 fits this pattern with a = x and b = 1, so it equals (x − 1)2. Solving a linear equation in one variable means expanding every bracket, collecting all x-terms on one side and constants on the other, then dividing to isolate x.

1. Expand both brackets: 5(3x + 4) = 15x + 20, and 8(6x + 7) = 48x + 56.

2. Substitute into the equation: 15x + 20 − 48x − 56 = 9x − 8, which simplifies to −33x − 36 = 9x − 8.

3. Collect the x-terms on one side and the constants on the other: −33x − 9x = −8 + 36, so −42x = 28.

4. Divide to isolate x: x = 28 ÷ (−42) = −2/3.

5. Substitute x = −2/3 into (x − 1)2: x − 1 = −2/3 − 1 = −5/3, and (−5/3)2 = 25/9.

Cross-check: expanding x2 − 2x + 1 directly with x = −2/3 gives x2 = 4/9, −2x = 4/3, and +1, so 4/9 + 12/9 + 9/9 = 25/9 — the same result by an independent route.