Question

Combine like terms. a. \(6 y+2 x-9 y\) b. \(5 x-3 y-11 x+13 y\) c. \(x-2 y+6 x+10 y\) d. \(12 x+13 y-16 x-4 y+2 x\)

Short answer

Question: Combine the like terms in the following expressions: a. \(6y+2x-9y\) b. \(5x-3y-11x+13y\) c. \(x-2y+6x+10y\) d. \(12x+13y-16x-4y+2x\) Answer: a. \(2x-3y\) b. \(-6x+10y\) c. \(7x+8y\) d. \(-2x+9y\)

Step-by-step solution

a. \(6y+2x-9y\)

Identify the like terms: \(6y\) and \(-9y\). Combine the like terms: \(6y-9y = -3y\). The final expression is: \(2x-3y\).

b. \(5x-3y-11x+13y\)

Identify the like terms: \(5x\) and \(-11x\), \(-3y\) and \(13y\). Combine the like terms: \(5x-11x = -6x\) and \(-3y+13y = 10y\). The final expression is: \(-6x+10y\).

c. \(x-2y+6x+10y\)

Identify the like terms: \(x\) and \(6x\), \(-2y\) and \(10y\). Combine the like terms: \(x+6x = 7x\) and \(-2y+10y = 8y\). The final expression is: \(7x+8y\).

d. \(12x+13y-16x-4y+2x\)

Identify the like terms: \(12x\), \(-16x\), \(2x\) and \(13y\) and \(-4y\). Combine the like terms: \(12x-16x+2x = -2x\) and \(13y-4y = 9y\). The final expression is: \(-2x+9y\).