Question

name:
combine the like terms in the express
(17) -3y + 12x - y - 3x
-4y + 9x
(18) 2x + 2y - 2x + y
2y + y
3y
(19) 5x + 6y + 7 + 3x + 2y - 2
8x + 8y + 5
(20) 13x - 5x - 4y + 15 + 3 - 2x
2(3x - 2y + 9)
(21) -15x + 2y - 5 + 16x - y + 6
x + 2y - y + 6

Explanation:

Problem (17): \(-3y + 12x - y - 3x\)

Step1: Group like terms

Group the \(x\)-terms and \(y\)-terms together: \((12x - 3x) + (-3y - y)\)

Step2: Combine like terms

For \(x\)-terms: \(12x - 3x = 9x\)
For \(y\)-terms: \(-3y - y = -4y\)
So the simplified expression is \(9x - 4y\) (or \(-4y + 9x\) as in the handwritten answer)

Step1: Group like terms

Group the \(x\)-terms and \(y\)-terms together: \((2x - 2x) + (2y + y)\)

Step2: Combine like terms

For \(x\)-terms: \(2x - 2x = 0\)
For \(y\)-terms: \(2y + y = 3y\)
So the simplified expression is \(3y\)

Step1: Group like terms

Group the \(x\)-terms, \(y\)-terms, and constant terms together: \((5x + 3x) + (6y + 2y) + (7 - 2)\)

Step2: Combine like terms

For \(x\)-terms: \(5x + 3x = 8x\)
For \(y\)-terms: \(6y + 2y = 8y\)
For constant terms: \(7 - 2 = 5\)
So the simplified expression is \(8x + 8y + 5\)

Answer:

\(9x - 4y\) (or \(-4y + 9x\))

Problem (18): \(2x + 2y - 2x + y\)