How do i solve this equation:5x^2 - 4(2x - 3)(x - 5)How do i solve double brackets in general?example: (a -b)(c + d) ?
First I'll start with the general, and then we'll apply it to the problem you have. For most double bracket problems you would work them out by FOIL-ing them. If you've never heard of it before, FOIL is the method given by: First Outside Inside Last These are the orders that you would multiply your terms, so lets take your example. (a-b)(c+d) FIRST, meaning the first numbers in the backets, in this case, we have a and c. so lets multiply them together. ac OUTSIDE, meaning the two numbers that form the outside of your problem, here we have a and d ad INSIDE, meaning the two numbers that form the inside of your problem, here we have -b and c. -bc LAST, the last number in each bracket, here we have -b and d -bd Now lets put them all together into one problem, and this would be your solution. In most cases, when you have one variable (just x usually), and youget to this point, you will have terms that you can combine, typically giving you a 3 term problem. If you have more than one variable (like x AND y) then you may have more. ac + ad - bc - bd Now, lets take a look at your problem. 5x^2 - 4(2x - 3)(x - 5) Let's apply our FOIL method to the numbers in the bracket. FIRST 2x*x 2x^2 OUTSIDE 2x*-5 -10x INSIDE -3*x -3x LAST -3*-5 +15 Now lets combine, what can we combine? How about the terms with x! 2x^2 -10x - 3x +15 Giving us 2x^2 -13x +15 BUT remember, that we're just dealing with the part in the bracket. The whole quantity is multiplied by 4! 8x^2 -52x +60 Then, remember that we also have the whole equation, which is now. (We use the parenthesis/brackets here because if you think about it, the problem is asking for 5x^2 less the QUANTITY of everything we did, so dont write it as 5x^2 - 8x^2 etc. you have to distribute the minus! 5x^2 - (8x^2-52x+60) So now our problem is 5x^2 - 8x^2 + 52x - 60 Simplify, and you have your answer! -3x^2 +52x -60
5x^2 - 4(2x - 3)(x - 5) 5x^2 - (8x - 12)(x - 5) 5x^2 - (8x^2 - 52x + 60 ) 5x^2 - 8x^2 + 52x - 60 -3x^2+ 52x - 60
Research the FOIL method for algebra. The remove the parentheses you use what's called the FOIL method. Multiply the first integers, outer, inner, and last
Well lets say this is the problem (5-3)(2*4) You would solve in the brackets first so 5-32 and 2*48 so now your problem looks like this (2)(8) since there is parenthesis/brackets you multiply 2*816 And thats how you solve double brackets. What are the different choices for x. Just subsitute the choices of x in the equation to get an answer.
