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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

1 answer

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. \( 2x^2 - 10x + 2 \)