combining like terms
1.) 10x+6y-5x
and
2.) 9x^2+10+4x^2+7
1. 0x+6y-5x = 5x+6y.
2. 9x^2+10+4x^2+7 = 13x^2+17.
To combine like terms, you need to first identify which terms are considered "like." "Like terms" refer to terms that have the same variables raised to the same exponent(s). In both expressions, identify the terms with the same variables and exponents and then combine them by adding or subtracting their coefficients.
1.) For 10x + 6y - 5x:
We have the terms 10x and -5x, which have the same variables (x) raised to the same exponent (1). Therefore, we can combine these terms by subtracting their coefficients:
10x - 5x = (10 - 5)x = 5x
The expression becomes: 5x + 6y
2.) For 9x^2 + 10 + 4x^2 + 7:
We have the terms 9x^2 and 4x^2, which have the same variables (x) raised to the same exponent (2). We can combine these terms by adding their coefficients:
9x^2 + 4x^2 = (9 + 4)x^2 = 13x^2
The expression becomes: 13x^2 + 10 + 7
Note that the terms 10 and 7 are constants and cannot be combined with the variable terms since they have different variables or no variable at all.
The final simplified expression is:
13x^2 + 17