Congratulations on making it to unit 2! In this lesson, we will combine like terms, and the method for finding like terms is straightforward. While you already know how to combine like terms, such as 7 and -4 (which would be 3 because that is the sum when adding them), the main focus is combining like terms with variables, such as 2x and 4x. Since these terms have the same variable and the same exponent (technically 1 because it is assumed to be there), these 2 could be combined to get the sum of 6x. Another way to think about it is that if we pick any number for x, they would be equal to each other. For example, you could say 2x+4x=6x, and then plug in a number like 2. Multiplying would get you 4+8=12, and then adding 4 and 8 would, of course, give you 12. A few things to consider when combining like terms are ensuring that you add them together, rather than multiplying them. Additionally, you must verify that the variable and exponents (if present) are the same. Even if both variables are x, such as 4x and 7x², you couldn't combine them due to the exponent in 7x². With that out of the way, let's get into some examples.
1: Simplify -4x+8x
Due to both terms in the expression having the same variable and exponents, they are therefore like terms. Because of that, the coefficients of -4 and 8 can be added to get 4, then put back by x, giving us 4x.
Answer: 4x
2: Simplify 6x+3x+9-4
Firstly, the like terms of 6x and 3x can be added to get the sum of 9x. Additionally, 9 and 4 are like terms due to both not having a variable or exponent, and 4 is then subtracted from 9 to get 5. Finally, you can put the combined terms together to get 9x+5.
Answer: 9x+5
3: Simplify 4x-2x+5y
For this, we can see that while the first two terms are similar due to having the same variables, the third is different due to it being y. With this information, we can combine the first 2 terms, subtracting -2x from 4x to get 2x, then keeping +5y at the end, giving us our answer of 2x+5y.
Answer: 2x+5y
4: Simplify -8x+4x²+11x
Firstly, we can see that while all 3 terms have the same variable of x, the 2nd term has x², meaning it CANNOT be combined with the 1st and 3rd ones. Therefore, the first and last term can be combined, which is -8x+11x, giving the sum of 3x. Finally, the 4x² can be added before or after the 3x, giving us the answer 4x²+3x. Usually, the expression with the larger exponent goes at the front in this case.
Answer: 4x²+3x
5: Simplify 4(2x-5y)-3x
In this expression, we have a different case than most, and we have to use the distributive property (which will be expanded on in the next lesson). Since there is an assumed multiplication between 4 and the terms in the expression, we can multiply 2x by 4 to get 8 and -5y and 4 to get -20y, giving us the expression 8x-20y-3x. Finally, we can combine the like terms of 8x and -3x to get 5x-20y.
Answer: 5x-20y
6: Simply 9y-6x-10y+3x+1y+3x
Firstly, we can manipulate the expression around so the like terms are by each other (they can move around because the order of adding/subtracting doesn't matter) to get 9y-10y+1y-6x+3x+3x. When adding and subtracting the terms with y, it cancels out to 0 with 9y-10y equaling -1y and then 1y being added to cancel out. Additionally, the x's cancel out with -6x+3x equaling -3x and then the second +3x then cancelling out, giving us our final answer of 0.
Answer: 0
1: Simplify 2x+8x-7x
2: Simplify 9x+2x-8+6
3: Simplify 10y-3y+8x³
4: Simplify 4x²+9-2x²
5: Simplify 14x-14x²-7x+2y
6: Simplify 6x+3x³-2x³+3x²
7: Simplify 15y²-10x²+9+4+10x²
8: Simplify 2y-1.5y+9x+½x
9: Simplify -6(4x-2x²)+28x
10: Simplify 0.5(12x+2x+4y)-4x
11: Simplify 4y³-½x+2y²+8y-4x²+½x
12: Simplify 2(4y+³⁄₂x-4z+8y)+2z+3z-0.5y
1: 3x
2: 11x-2
3: 8x³+7y
4: 2x²+9
5: -14x²+7x+2y
6: x³+3x²+6x
7: 15y²+13
8: 9.5x+0.5y
9: 12x²+4x
10: 3x+2y
11: -4x²+4y³+2y²+8y
12: 3x+23.5y-3z