#Simplifying expressions plus#So we have 2 of the thing plus 1 of the thing, and of course whenever you have 2 of anything plus 1 of the same thing, you get 3 of that thing, so that's how we simplify that. But the two terms are actually like terms, because the variable part, x to the 5th, y to the 4th, z to the 7th, those are identical between the two terms. In that final one, notice that thing is awfully complicated. So when we add, we just get 3 plus 3, which is 6, 6y squared. 3y squared + 3y squared, those are like terms, in fact they're identical. So for example, 15y-8y, both of those are like terms, the variable part is just y, so we can subtract. And in essence, we're just adding or subtracting the coefficients. The number one algebraic simplification rule, we can combine like terms by addition or subtraction. Now what do we mean by like terms? Like terms are any two terms with the same variable part, if they differ at all, they differ only in coefficients. And of course, we can 3x + 5x using the distributive law, because they are like terms. Every single number on the number line would obey this particular rule. So what we're saying here is, we have a rule that's true for all numbers. Now let's think about this for a minute, we've said one expression, 3x + 5x, is equal to another expression, 8x. But suppose we have to simplify 3x + 5x, of course, 3x + 5x = 8x. Now of course, this is a very easy question, the test is not gonna ask something this basic. So suppose we are asked, simplify 3x + 5x. Our first topic in Algebraic Expressions is simplifying expression.
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