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Topic: **Explain the problem solving method****Question:**
can somebody explain to me step by step how you would go about solving this problem using foil method? i have others but its just to get an idea.
(4a - 5b)(3a - 2b)
thank you!

May 21, 2019 / By Gretchen

(4a-5b) (3a-2b) first you multiply the first two terms (4a) (3a) = 12a² Next multiply the first term from the first equation times the second term from the second equation (4a) (-2b) = -8ab Then multiply the second therm from the first equation times the first term from the second equation ( -5b) (3a)= -15ab After that multiply the second term from the firts equation times the second term from the second equation (-5b) (-2b)= 10b² Later solve the problem combining the like terms 12a²-8ab-15ab+10b² and your answer will be: 12a²-23ab+10b²

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Despite the preamble of your question, the actual problem you posed did NOT have the form of "a radical number [multiplied by] a whole number"; it was instead of the form you said that you knew how to handle, namely two radicals multiplied together. As such, radical 2 x radical 3 = radical 6. If however, you really wanted to know about: radical(2) times 3, that could be written as radical(18). Why 18? Because when taking the whole number 3 under the radical sign, it must itself be squared. However, this would be considered a retrograde step. Most people will take out an obvious squared number out from under a radical sign, so that the radical itself only deals with quantities whose OWN square roots can not readily be taken. Live long and prosper.

i lurrveee foil foil stands for firsts, outers, inners, lasts. so that would be the order you multiply the numbers in. 1. write the equation (4a - 5b)(3a - 2b) 2. multiply the first terms in each parenthesis; which would be 4a and 3a (4a - 5b)(3a - 2b) 4a x 3a = 12a^2 (it is squared because there are two a's being multiplied together) 2. multiply the outer terms in each parenthesis; 4a and -2b 4a x (-2b) = -8ab so far your equation is 12a^2 - 8ab 3. multiply the inner terms in each parenthesis; -5b and 3a (-5b) x 3a = -15ba so far your equation is 12a^2 - 8ab - 15ba 4 multiply the last terms in each parenthesis; -5b and -2b (-5b) x (-2b) = +10b^2 your equation is 12a^2 - 8ab - 15ba +10b^2 5 combine like terms. the first terms you are going to combine are -8ab and -15ba. even though the a and b are in a different order, you can still combine them. so. -8ab + (-15ba) = -23ab you don't square ab because you're adding, not multiplying so your equation so far is 12a^2 - 23ab + 10b^2 6. depending on on how your teacher likes the equation, you may have to move the squares to the front and put them in alphabetical order soo... 12a^2 + 10b^2 - 23ab is your final equation. (:

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4a - 5b 3a - 2b - - - - - - 12a^2 - 15ab . . . . .- 8 ab + 10b^2 - - - - - - - - - - - - - - - 12a^2 - 23ab + 10b^2 Multiply each term in one expression by each term in the other, then combine like terms Doing the multiplication this way makes it easy to combine like terms because they end up in the same column Don't lean too heavily on FOIL, which works ONLY when multiplying two binomials

👍 41 | 👎 -2

foil stands for first, outer, inner, last so you multiply in that order for example (x+y)(m+n)= mx + nx + my + ny for your example the answer would be: (4a - 5b)(3a - 2b) = 12a^2 - 8ab - 15 ab + 10b^2 = 12a^2 - 23ab + 10b^2

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F firsts . . . . . . . . 4a*3a O outsides . . . . . 4a*(-2b) I insides . . . . . . . (-5b)*3a L lasts . . . . . . . . . (-5b)*(-2b) so u multiply the 1st ones in each, then the outside terms, then inside terms, then the last ones in each and add all together 12a^2 - 8ab - 15ab + 10b^2 12a^2 + 10b^2 - 23ab

👍 23 | 👎 -14

No problem! It's not as hard as it looks! :) Here's how to do it: Start with the first part: 3(x-2) multiply the 3 by the x multiply the 3 by the -2 (don't forget the negative!) so for the first parenthesis you get.... (3x-6) Then do the second part: 4(x-1) multiply the 4 by the x multiply the 4 by the -1 (again, don't forget the negative!) so you get........ (4x-4) Then add the like terms together - in other words, add the numbers together (called constants), and add the x terms together. So the answer is: 4x + 3x + -4 + -6 which reduces to: 7x - 10 Hope this helps! Good luck!!!

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