Question

simplify each algebraic expression by combining like terms.
expression | expression by combining like terms
$4z + 2y - 3z + z + 5y$ |
$2z + 3y + 5z - 2y + z - y$ |

Explanation:

Step1: Group like terms (first expression)

Group $x$-terms and $y$-terms:
$(4x - 3x + x) + (2y + 5y)$

Step2: Combine $x$-terms (first expression)

Calculate sum of $x$-terms:
$4x - 3x + x = (4-3+1)x = 2x$

Step3: Combine $y$-terms (first expression)

Calculate sum of $y$-terms:
$2y + 5y = (2+5)y = 7y$

Step4: Group like terms (second expression)

Group $x$-terms and $y$-terms:
$(2x + 5x + x) + (3y - 2y - y)$

Step5: Combine $x$-terms (second expression)

Calculate sum of $x$-terms:
$2x + 5x + x = (2+5+1)x = 8x$

Step6: Combine $y$-terms (second expression)

Calculate sum of $y$-terms:
$3y - 2y - y = (3-2-1)y = 0y = 0$

Answer:

1. $2x + 7y$
2. $8x$