Video instructions and help with filling out and completing Which Form 2220 Summary

Instructions and Help about Which Form 2220 Summary

In this video we're going to go over a basic introduction a slash overview of college algebra so let's begin with some basics what is x squared times X to the fifth power what do you do to the exponents when you multiply common bases x squared times X to the fifth power is X to the seventh power when you multiply by a similar base you are allowed to add the exponents x squared can be thought of as x times X you multiply 2x variables together X to the fifth power is basically 5x variables together combined you have a total of seven X variables which represents that what about division what is X to the fifth power divided by x squared when you divide you need to subtract the top number by the bottom number 5 minus 2 is 3 again if you expand it it can make sense X to the fifth power is 5 X is multiplied to each other x squared is just two x's so you can cancel two of them which leaves 3 on top so let's try another example what is X to the fourth divided by X to the seventh so taking the top number subtracting the bottom number 4 minus 7 is negative 3 and whenever you have a negative exponent you can move the X variable from the top to the bottom and as you do that the sign will change then negative 3 will change it into a positive dream so this is the same as 1 over X cube now let's expand it X to the fourth is basically 4 X variables multiplied to each other X to the seventh represents 7x variables we can cancel floor on top for the bottom and so we're left with 3 on the bottom which is X cube now what is X cubed raised to the fourth power whenever you raise one exponent to another exponent you are allowed to multiply them three times four is 12 so the answer is X to the 12 power one way you could think about it imagine X cube raised to the fourth power is equivalent to four X cubes multiplied to each other that's what it really represents and each X cube represents the multiplication of three X variables so when you combine them you have a total of twelve X variables multiplied to each other so that's why you get X to the 12 anytime you raise something to the zero power it's always equal to one that's something you just have to commit to memory now let's talk about simplifying expressions and combining like terms if you were to see something like this on the test 5x + 3 + 7 X - 4 how would you simplify this expression notice the 5x and a 7x are like terms they both carry the variable X 5 plus 7 is 12 so 5x plus 7x is 12x now these two don't have an X variable attached to it so they're similar to each other 3 plus negative 4 is the same as 3 minus 4 which is negative one go ahead and try this one 3x squared + 6 X + 8 + 9 x squared + 7 X - 5 feel free to take a minute pause the video and work on this example so these two are like terms 3 plus 9 is 12 we can add these to 6 plus 7 is 13 and then we can add these two eight plus negative five or eight minus five is positive three here's another one that we could try five x squared minus three X plus seven minus four x squared minus 8x minus eleven now the first thing we should do is we should distribute this negative sign to each of these three terms before we combine like terms if you want to avoid making mistakes now we don't have a negative sign in front of the first set of terms inside the first parenthesis so we could just open it so what we have now is five x squared minus three X plus seven and if we distribute the negative sign to everything on the right all the signs will change the positive 4x squared will now become negative four x squared the negative 8x will now change to positive 8x and the same is true for the eleven it's going to change from negative eleven to positive 11 so now let's combine like terms 5x squared minus 4x squared is one x squared negative three plus eight which is the same as 8 minus 3 is positive five and 7 plus 11 is 18 so you're going to get this now what if we want to multiply two expressions instead of adding and subtracting polynomials by the way this is a monomial that's one term two terms represent a binomial three terms represent a trinomial and if you have like many terms you can simply call it a polynomial it's good to be familiar with those expressions so here we're multiplying two binomials we need to use something called foil in foil the first letter F is for the first part we multiply the first two terms 3x times 2x is 6x squared and then you multiply the term only outside 3x times negative 6 which is negative 18x and then the ones on the inside negative 5 times 2x that's negative 10x and then the last ones negative 5 times negative 6 which is positive 30 so now let's combine the two terms in the middle since they're like terms negative 18x plus negative 10x is negative 28 X so this is the answer now how can we expand an expression that looks like this what would you do if you saw BAM assess to expand it the square means that we have two 2x minus 5 factors multiplied to each other so