To solve the expressions in the image, we simplify each step-by-step:
1. $(5x^2 + 3x - 2) + (2x^2 - 6x + 4)$
Combine like terms:
$5x^2 + 2x^2 + 3x - 6x -2 +4 = 7x^2 -3x +2$
2. $(3x^2 -2x +1) - (x^2 +4x -5)$
Distribute the negative sign and combine like terms:
$3x^2 -2x +1 -x^2 -4x +5 = 2x^2 -6x +6$
3. $2(4x^2 -3x +2)$
Multiply each term by 2:
$8x^2 -6x +4$
4. $(x +3)(x -2)$
Expand using FOIL:
$x^2 -2x +3x -6 = x^2 +x -6$
5. $(2x -1)^2$
Use the square of a binomial formula $(a-b)^2=a^2-2ab+b^2$:
$(2x)^2 -2(2x)(1) +1^2 =4x^2 -4x +1$
Final Results:
- $7x^2 -3x +2$
- $2x^2 -6x +6$
- $8x^2 -6x +4$
- $x^2 +x -6$
- $4x^2 -4x +1$
$\boxed{7x^2 -3x +2}$, $\boxed{2x^2 -6x +6}$, $\boxed{8x^2 -6x +4}$, $\boxed{x^2 +x -6}$, $\boxed{4x^2 -4x +1}$ (depending on which one is needed; if all, list as above).
If the question expects a single answer (unlikely, but if forced), perhaps the first one is the main, but more likely, all simplified forms are required. For conciseness, here are the boxed answers for each:
$\boxed{7x^2 - 3x + 2}$
$\boxed{2x^2 - 6x + 6}$
$\boxed{8x^2 - 6x + 4}$
$\boxed{x^2 + x - 6}$
$\boxed{4x^2 - 4x + 1}$
(Note: If the user intended one specific expression, clarify, but given the image has 5, these are all simplified.)
Answer: $\boxed{7x^2 -3x +2}$ (taking the first expression as an example; adjust based on context)
But to cover all, the simplified forms are as listed above. If a single answer is needed, perhaps the first is intended: $\boxed{7x^2 -3x +2}$
$\boxed{7x^2 - 3x + 2}$
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