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# Multiplying monomials by polynomials

CCSS.Math:

## Video transcript

multiply negative 4x squared by the whole expression 3x squared + 25 X - 7 so if you multiply anything times a whole expression you really just use the distributive property to multiply each term of the expression by the negative 4x squared so we're gonna have to distribute this negative 4x squared over every term in the expression so first we can start with negative 4x squared squared times 3x squared so we can write that we're going to have negative 4x squared times 3x squared + 2 that we're going to add negative 4x squared times 25 x times 25 X and to that we're going to add negative 4x squared times negative 7 times negative 7 so let's just simplify this a little bit now we can obviously swap the order we're just multiplying negative 4 times x squared times 3 times x squared and actually I'll do out every step eventually you can do some of this in your head this is the exact same thing as negative 4 times 3 times x squared times x squared and what is that equal to well negative 4 times 3 is negative 12 and x squared times x squared same base we're taking the product that's going to be X to the fourth so this right here is negative 12 X to the fourth now let's think about this term over here this term over here this is the same thing as and of course we have this Plus out here we have this plus and then this part right here is the exact same thing as 25 25 times negative 4 times x squared times X so let's just multiply the numbers out here these were the coefficients 25 times negative 4 is negative 100 so it'll be plus negative 100 or we could just say it's minus 100 and then we have x squared times X or x squared times X to the first power same base we can add the exponents 2 plus 1 is 3 so this is negative 100 X to the third power and then let's look at this last term over here we have negative 4 x squared so this is going to be plus that's this plus right over here we have we have negative four we can multiply that times negative seven and then multiply that times x squared I'm just changing the order in which we multiply it so negative 4 times negative 7 is positive 28 positive 28 and then I'm going to multiply that times the x squared times the x squared and there's no simplification to do no like terms these are different powers of X so we are done