<p>Like Terms "Like terms" are terms whose variables and exponents are the same. In other words, terms that are "like" each other. Note: the coefficients (the numbers you multiply by, such as "5" in 5x) can be different.</p><p>Example: 7x x -2x</p><p>Are all like terms because the variables are all x Example: (1/3)xy2 -2xy2 6xy2 </p><p>Are all like terms because the variables are all xy2</p><p>Unlike Terms If they are not like terms, they are called "Unlike Terms": Unlike Terms Why they are "Unlike Terms" ← these are all unlike terms -3xy -3y 12y2 (xy, y and y2 are all different)</p><p>Combining Like Terms You can add or subtract like terms together to make one term: Example: 7x + x They are both like terms, so you can just add them by adding the coefficients, but do NOT add or multiply the variables: 7x + x = 8x How should you handle expressions or equations with lots of terms like: 3x2 - 7 + 4x3 - x2 + 2</p><p>The 1st thing to do is to re-arrange the expression by either putting like terms next to each other or grouping them together with parenthesis. Make sure you correctly re-write your negatives or subtraction and your positives or addition. So combining or regrouping the expression 3x2 - 7 + 4x3 - x2 + 2 results in (3x2 - x2) + (4x3) + (2 - 7)</p><p>Next, add or subtract like terms: 2x2 + 4x3 – 5</p><p>Multiplying Like Terms We somewhat covered this with exponents. </p><p>The key is to make sure that you use the correct rules of multiplying exponents and that you multiply all coefficients by all coefficients. What do I mean by that?</p><p>Let's forget exponents for a moment.</p><p>Say you have 3y × 2y. This is much different from 3y + 2y. Why?</p><p>In the addition example, we:</p><p>Add the coefficients and we do NOT multiply the variables = 5y</p><p>With multiplication, we must multiply both the variables and the coefficients. In long form: 3y × 2y = 3 × y × 2 × y</p><p>If you rearrange this, it becomes: 3×2×y×y</p><p>Now multiply similar terms you get: 6y2</p><p>Reminder:</p><p>Rules of multiplying exponents: am×an = am+n (am)n = a(mn)</p><p>Dividing Like Terms</p><p>The key is to make sure that you use the correct rules of dividing exponents and that you divide all coefficients by all coefficients. What do I mean by that?</p><p>Let's forget exponents for a moment.</p><p>Say you have 4y ÷ 2y. </p><p>We must divide both the variables and the coefficients. In long form:</p><p>4y ÷ 2y = </p><p>Essentially, we REDUCE or combine like terms. Our goal, is to get as many "1's" as possible. Here, the 4 is reduced by the 2 and the y's cancel each other out so we are left with just:</p><p>2</p><p>Reminder:</p><p>Rules of dividing exponents: am / an = am-n</p><p>Simplify the following:</p><p>2y3 + x2 y2 + x</p><p>Your 1st inkling is going to be to reduce the numerator and the denominator. Since there is addition and subtraction – DON'T</p><p>Let's plug in #'s to show this. Make y = 2 and x = 3</p><p>2(2 3 ) + 3 2 = 2(8) + 9 Can you reduce anything in the num and denom? 22 + 3 4+3</p><p>1st – let's calculate the real answer which is 25/7. </p><p>Now let's see what happens if we reduce the 9 and the 3. So now make it:</p><p>16+3 = 19 4+1 5. This is clearly different from 25/7. What if we multiplied one of the terms in the numerator by 4 and one in the denominator by 2, could we reduce the 4 and the 2?</p><p>2(2 3 ) + 3 2 (4) This becomes: 2(8) + 9(4) = 16+36 = 52 = 26 22 + 3(2) 4+6 10 10 5</p><p>If we reduced the 4 and the 2, we would have:</p><p>2(2 3 ) + 3 2 ( 2 ) This becomes: 2(8) + 9(2) = 16+18 = 34 22 + 3(1) 4+3 7 7</p><p>You can only reduce an expression if it is multiplied throughout the entire numerator and the entire denominator:</p><p>4[ 2(2 3 ) + 3 2 ] This becomes: 4[2(8) + 9] = 4[16+9] = 4[25] = 100 = 50 2[22 + 3] 2[4+3] 2[7] 14 14 7</p><p>If we reduced the 4 and the 2, we would have a 2 in the numerator and a 1 in the denominator and you would get:</p><p>50/7 which not by coincidence, is twice the value of our original expression of</p><p>2(2 3 ) + 3 2 = 25/7 22 + 3</p><p>Remember – if you have a HUGE division expression or fraction with lots of terms, you can only reduce it if the numerator and denominator have a term that is multiplied across every term in the numerator and denominator. </p>