1 00:00:00,822 --> 00:00:03,053 Multiply negative four x squared by 2 00:00:03,053 --> 00:00:04,623 the whole expression 3 00:00:04,623 --> 00:00:06,337 three x squared plus twenty five x 4 00:00:06,337 --> 00:00:08,060 minus seven 5 00:00:08,060 --> 00:00:09,340 So if you multiply anything 6 00:00:09,340 --> 00:00:11,084 times a whole expression you really just use 7 00:00:11,084 --> 00:00:13,605 the distributive property to multiply each term 8 00:00:13,605 --> 00:00:15,107 of the expression by 9 00:00:15,107 --> 00:00:16,485 the negative four x squared 10 00:00:16,485 --> 00:00:17,952 so we're going to have to distribute 11 00:00:17,952 --> 00:00:20,402 this negative four x squared 12 00:00:20,402 --> 00:00:22,473 over every term in the expression. 13 00:00:22,473 --> 00:00:23,513 So first we can start with 14 00:00:23,513 --> 00:00:25,462 negative four x squared times 15 00:00:25,462 --> 00:00:26,852 three x squared 16 00:00:26,852 --> 00:00:27,877 so we can write that 17 00:00:27,877 --> 00:00:30,332 we're gonna have negative four x squared 18 00:00:30,332 --> 00:00:32,765 times three x squared 19 00:00:32,765 --> 00:00:35,057 and to that we're going to add 20 00:00:35,057 --> 00:00:39,810 negative four x squared times twenty five x 21 00:00:39,810 --> 00:00:41,761 times twenty five x 22 00:00:41,761 --> 00:00:44,509 and to that we're going to add 23 00:00:44,509 --> 00:00:49,204 negative four x squared times negative seven 24 00:00:49,204 --> 00:00:51,992 times negative seven 25 00:00:51,992 --> 00:00:53,772 So let's just simplify this a little bit 26 00:00:53,772 --> 00:00:56,451 Now we can obviously swap the order 27 00:00:56,451 --> 00:00:58,313 we're just multiplying negative four times 28 00:00:58,313 --> 00:01:00,328 x squared times three times x squared 29 00:01:00,328 --> 00:01:01,403 and actually I'll do out every step 30 00:01:01,403 --> 00:01:03,296 eventually you can do some of this in your head 31 00:01:03,296 --> 00:01:05,932 this is the exact same thing as negative four 32 00:01:05,932 --> 00:01:09,661 times three times x squared times 33 00:01:09,661 --> 00:01:11,165 x squared 34 00:01:11,165 --> 00:01:12,616 And what is that equal to? 35 00:01:12,616 --> 00:01:14,551 well negative four times three 36 00:01:14,551 --> 00:01:16,422 is negative twelve 37 00:01:16,422 --> 00:01:17,918 and x squared times x squared 38 00:01:17,918 --> 00:01:19,697 same base, we're taking the product 39 00:01:19,697 --> 00:01:21,262 that's going to be x to the fourth 40 00:01:21,262 --> 00:01:23,007 so this right here is 41 00:01:23,007 --> 00:01:24,999 negative twelve x to the fourth 42 00:01:24,999 --> 00:01:27,405 Now let's think about this term over here 43 00:01:27,405 --> 00:01:28,522 this term over here 44 00:01:28,522 --> 00:01:30,295 This the same thing as 45 00:01:30,295 --> 00:01:32,177 And of course we have this plus out here 46 00:01:32,177 --> 00:01:33,391 We have this plus 47 00:01:33,391 --> 00:01:34,692 And then this part right here is 48 00:01:34,692 --> 00:01:36,875 the exact same thing as twenty five 49 00:01:36,875 --> 00:01:39,924 twenty five times negative four 50 00:01:39,924 --> 00:01:43,425 times x squared times x 51 00:01:43,425 --> 00:01:46,530 So let's just multiply the numbers out here 52 00:01:46,530 --> 00:01:47,932 These were the coefficients. 53 00:01:47,932 --> 00:01:49,884 Twenty five times negative four is 54 00:01:49,884 --> 00:01:51,001 negative a hundred. 55 00:01:51,001 --> 00:01:52,229 So it'll be plus negative a hundred 56 00:01:52,229 --> 00:01:55,071 or we could just say it's minus one hundred 57 00:01:55,071 --> 00:01:56,093 And then we have x squared times x 58 00:01:56,093 --> 00:01:59,953 or x squared times x to the first power 59 00:01:59,953 --> 00:02:01,875 Same base, we can add the exponents. 60 00:02:01,875 --> 00:02:03,992 Two plus one is three. 61 00:02:03,992 --> 00:02:08,189 So this is negative a hundred x to the third power 62 00:02:08,189 --> 00:02:10,678 And then let's look at this last term over here 63 00:02:10,678 --> 00:02:12,293 We have negative four x squared 64 00:02:12,293 --> 00:02:13,481 So this is going to be plus 65 00:02:13,481 --> 00:02:14,788 That's this plus right over here 66 00:02:14,788 --> 00:02:15,896 We have 67 00:02:15,896 --> 00:02:18,204 We have negative four 68 00:02:18,204 --> 00:02:20,580 We can multiply that times negative seven 69 00:02:20,580 --> 00:02:22,896 And then multiply that times x squared 70 00:02:22,896 --> 00:02:23,891 I'm just changing the order 71 00:02:23,891 --> 00:02:25,386 in which we multiply 72 00:02:25,386 --> 00:02:27,481 So negative four times negative seven is 73 00:02:27,481 --> 00:02:28,976 positive twenty eight. 74 00:02:28,976 --> 00:02:30,480 Positive twenty eight 75 00:02:30,480 --> 00:02:31,944 and then I'm gonna multiply that times 76 00:02:31,944 --> 00:02:33,826 the x squared 77 00:02:33,826 --> 00:02:35,151 times the x squared 78 00:02:35,151 --> 00:02:36,574 There's no simplification to do 79 00:02:36,574 --> 00:02:37,640 No like terms 80 00:02:37,640 --> 00:02:39,321 These are different powers of x. 81 00:02:39,321 --> 99:59:59,999 So we are done.