Question

Solve the following expressions by collecting like terms
x(2x+3y-4)-x²+4xy-12
25+3t-s+5t+4s
4(p-5)+3(p+1)
-3x+4+2x²-7x-2

Answer 1

Let's solve each expression one by one by collecting like terms.

1. **Expression**: \( x(2x + 3y - 4) - x^2 + 4xy - 12 \)

Expand the expression:
\[
x(2x) + x(3y) - x(4) - x^2 + 4xy - 12 = 2x^2 + 3xy - 4x - x^2 + 4xy - 12
\]

Combine like terms:
\[
(2x^2 - x^2) + (3xy + 4xy) + (-4x) - 12 = x^2 + 7xy - 4x - 12
\]

**Final result**: \( x^2 + 7xy - 4x - 12 \)

2. **Expression**: \( 25 + 3t - s + 5t + 4s \)

Combine like terms:
\[
25 + (3t + 5t) + (-s + 4s) = 25 + 8t + 3s
\]

**Final result**: \( 25 + 8t + 3s \)

3. **Expression**: \( 4(p - 5) + 3(p + 1) \)

Expand the expression:
\[
4p - 20 + 3p + 3 = 4p + 3p - 20 + 3
\]

Combine like terms:
\[
(4p + 3p) + (-20 + 3) = 7p - 17
\]

**Final result**: \( 7p - 17 \)

4. **Expression**: \( -3x + 4 + 2x^2 - 7x - 2 \)

Combine like terms:
\[
2x^2 + (-3x - 7x) + (4 - 2) = 2x^2 - 10x + 2
\]

**Final result**: \( 2x^2 - 10x + 2 \)

In summary, the collected results are:
1. \( x^2 + 7xy - 4x - 12 \)
2. \( 25 + 8t + 3s \)
3. \( 7p - 17 \)
4. \( 2x^2 - 10x + 2 \)