Simplify (5x² + 2x − 1) − 4(3 − 8x + 2x²).

Step-by-step solution

1. 1

   Distribute the −4 across all three terms. Each term inside the bracket changes sign as well as size:

   $-4(3)=-12,\qquad -4(-8x)=+32x,\qquad -4\left(2x^{2}\right)=-8x^{2}$

   The middle one is the trap: subtracting four copies of $-8x$ adds $32x$.

2. 2

   Write the whole expression bracket-free.

   $5x^{2}+2x-1-12+32x-8x^{2}$

3. 3

   Group the like terms. Sort by degree so nothing is missed:

   $\left(5x^{2}-8x^{2}\right)+(2x+32x)+(-1-12)$

4. 4

   Combine each group.

   $-3x^{2}+34x-13$

   $\boxed{-3x^{2}+34x-13}$

5. 5

   Check with a test value. At $x=1$: the original is $(5+2-1)-4(3-8+2)=6-4(-3)=6+12=18$, and the answer gives $-3+34-13=18$ ✓. At $x=0$: original $=-1-12=-13$, answer $=-13$ ✓. Two independent checks make a sign slip very unlikely.