A3-b3 formula

Table of Contents • • • • • • • a3 b3 Formula and a3 b3 Formula Proof a3 b3 Formula is a polynomial equation with two variables. It is an equation in the form P=0, where P is the polynomial. A polynomial is a mathematical expression that solely uses the operations of subtraction, addition, multiplication, and positive-integer powers of variables. It is made up of indeterminates, also known as variables, such as x, y and z, and numeric coefficients. The a3 b3 Formula are as follows. a 3 + b 3 = (a + b)(a 2 – ab + b 2) a 3 – b 3 = (a – b)(a 2 + ab +b 2) Proof of a3 + b3 formula As we know that: (a + b) 3 = a 3 + b 3 + 3ab(a + b) Hence: a 3 + b 3 = (a + b) 3 – 3ab(a + b) Taking (a + b) common in RHS, we get a 3 + b 3 = (a + b)[(a + b) 2 – 3ab] a 3 + b 3 = (a + b)[(a 2 + b 2 + 2ab) – 3ab] a 3 + b 3 = (a + b)(a 2 + b 2 + 2ab –3ab) a 3 + b 3 = (a + b)(a 2 – ab + b 2) Proof of a3 – b3 formula As we know that: (a – b) 3 = a 3 – b 3 – 3ab(a – b) Hence: a 3 – b 3 = (a – b) 3 + 3ab(a – b) Taking (a – b) common in RHS, we get a 3 – b 3 = (a – b)[(a – b) 2 + 3ab] a 3 – b 3 = (a – b)[(a 2 + b 2 – 2ab) + 3ab] a 3 – b 3 = (a – b)(a 2 + b 2 – 2ab + 3ab) a 3 – b 3 = (a – b)(a 2 + b 2 + ab) See Also: Solved Questions and Answers for a3 b3 Formula In this section, we have provided a few solved questions that involve usage of a3 b3 Formula. Q1) If a = 7 and b = 3, Find the value of (a 2 – ab + b 2) using a3 b3 Formula Ans) Given: a = 7 and b = 3 As per the given data, a + b = 10 And a 3 + b 3 ...

Lets take an example a 3 + b 3 + c 3 − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac) 2 3 + 3 3 + 4 3 – 3(2)(3)(4) = (2 + 3 + 4) (2 2 + 3 2 + 4 2 – (2)(3) – (3)(4) – (4)(2)) 8 + 27 + 64 – 72 = (9) (4 + 9 + 16 – 6 – 12 – 8) 99 – 72 = (9) (29 – 26) 27 = (9) (3) 27 = 27 If a + b + c = 0 Then, a 3 + b 3 + c 3 − 3abc = (a + b + c) (a 2 + b 2 + c 2 − ab − bc − ac) a 3 + b3 + c 3 − 3abc = (0) (a 2 + b 2 + c 2 − ab − bc − ac) a 3 + b 3 + c 3 − 3abc = 0 a 3 + b 3 + c 3 = 3abc Check

a^3+b^3 Formula The a 3 + b 3 formula is called the sum of cubes (of two numbers) formula. The a cube plus b cube formula is used to find the sum of the two cubes without actually computing the cubes. Also, it is used to factorize the binomials of cubes. Here, we will be discussing the different aspects of the a 3 + b 3 formula, along with solved examples, and understand where this identity can be applied. What is a^3+b^3 Formula? The a 3 + b 3 formula or the difference of a 3 + b 3 = (a + b) (a 2 - ab + b 2) Are the signs confusing? The following trick helps! ☛Also Check: • • • Let us learn the a 3 + b 3 formula with a few solved examples. The a 3 + b 3 formula can be verified, by 2 - ab + b 2) and see whether you get a 3 + b 3. Proof of a Cube plus b Cube Formula Let us verify the "a cube plus b cube" formula here. To prove or verify that a 3 + b 3 = (a + b) (a 2 - ab + b 2) we need to prove here LHS = RHS. LHS = a 3 + b 3 On simplifying the RHS side we get, = (a + b) (a 2 - ab + b 2) On multiplying the a and b separately with (a 2 - ab + b 2) we get = a (a 2 - ab + b 2) + b(a 2 - ab + b 2) = a 3 - a 2b + ab 2 + a 2b - ab 2 + b 3 = a 3 - a 2b + a 2b + ab 2- ab 2 + b 3 = a 3 - 0 + 0 + b 3 = a 3 + b 3 Hence, a 3 + b 3 = (a + b) (a 2 - ab + b 2). Use our free online calculator to solve challenging questions. With Cuemath, find solutions in simple and easy steps. Examples on a^3 + b^3 Formula Example 1: Find the value of 102 3 + 8 3 by using the a^3+b^3 formula. Solution: To...

There are a variety of different ways to combine columns in Excel, and I am going to show you five different formulas that you can use to combine multiple columns into one.Three of these formulas will combine columns horizontally, and two of them will combine columns vertically. Directly below are quick instructions for combining columns, but also look further below for detailed examples, as well as additional ways of combining columns. To combine columns horizontally in Excel, follow these steps: • Type an equals sign and then a column reference, such as =A3:A12 to specify the first column to combine • Type an ampersand ( &) • Type the address of the other column that you want to combine with, such as B3:B12 • Press enter on the keyboard. The full formula will look like this: =A3:A12&B3:B12 (If you are using an older version of Excel, you will need to hold "Ctrl" and "Shift" on the keyboard before pressing "Enter". If you do this, curly brackets will appear before and after your formula, like this: • Optional: If you want, you can add special characters between the combined columns by using additional ampersands, and any character that you want between quotation marks, like this =A3:A12&""&B3:B12 (See detailed instructions below for how to add spaces or special characters between the columns) To combine columns vertically in Excel, follow these steps: • Method 1: Enter the following formula in a blank cell / column, to combine columns vertically: =IF(A3"",A3,INDIRECT("B"...

You can use a Here’s a formula that uses two cell ranges : =SUM(A2:A4,C2:C3) sums the numbers in ranges A2:A4 and C2:C3. You’d press Enter to get the total of 39787. To create the formula: • Type =SUM in a cell, followed by an opening parenthesis (. • To enter the first formula range, which is called an argument (a piece of data the formula needs to run), type A2:A4 (or select cell A2 and drag through cell A6). • Type a comma (,) to separate the first argument from the next. • Type the second argument, C2:C3 (or drag to select the cells). • Type a closing parenthesis ), and then press Enter. Each argument can be a range, a number, or single cell references, all separated by commas. • =SUM(A2:A4,2429,10482) • =SUM(4823,A3:A4,C2:C3) • =SUM(4823,12335,9718,C2:C3) • =SUM(A2,A3,A4,2429,10482) Tip: If you need to sum columns or rows of numbers next to each other, Give it a try If you want to play around with our sample data, here’s some data to use. You can see how the SUM function works by copying the following table into a worksheet and pasting it into cell A1. Data -5 15 30 '5 TRUE Formula Description Result =SUM(3, 2) Adds 3 and 2. 5 =SUM("5", 15, TRUE) Adds 5, 15 and 1. The text value "5" is first translated into a number, and the logical value TRUE is first translated into the number 1. 21 =SUM(A2:A4) Adds the values in cells A2 through A4. 40 =SUM(A2:A4, 15) Adds the values in cells A2 through A4, and then adds 15 to that result. 55 =SUM(A5,A6, 2) Adds the values in cells...

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