Simplify the following expressions.

1. 5(3s - 2) + 12x
2. 7(3y -5) + 2 (4y + 3)

1 answer

Let's simplify each expression step by step:

  1. Expression: \(5(3s - 2) + 12x\)

    Start by distributing the \(5\) into the parentheses: \[ 5 \times 3s - 5 \times 2 = 15s - 10 \] Now, substitute this back into the expression: \[ 15s - 10 + 12x \] The simplified expression is: \[ 15s + 12x - 10 \]

  2. Expression: \(7(3y - 5) + 2(4y + 3)\)

    First, distribute the \(7\) and \(2\) into their respective parentheses: \[ 7 \times 3y - 7 \times 5 = 21y - 35 \] \[ 2 \times 4y + 2 \times 3 = 8y + 6 \] Now, combine these two results: \[ 21y - 35 + 8y + 6 \] Combine like terms: \[ (21y + 8y) + (-35 + 6) = 29y - 29 \] The simplified expression is: \[ 29y - 29 \]

In summary:

  1. \(15s + 12x - 10\)
  2. \(29y - 29\)