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To find: x 3 + 8y 3 Given: x + 2y = 6 xy = 2 Using a plus b whole cube formula, (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 Here, a = x; b = 2y Therefore, (x + 2y) 3 = x 3 + 3 × x 2 × (2y) + 3 × x × (2y) 2 + (2y) 3 (x + 2y) 3 = x 3 + 6x 2 y + 12xy 2 + 8y 3 6 3 = x 3 + 6xy(x + 2y) + 8y 3 216 = x 3 + 6 × 2 × 6 + 8y 3 x 3 + 8y 3 = 144
Sample Math Problems. Question: Use the formula to expand: ( x+y)^ {3} (x+y)3. Solution: x^ {3} +3x^ {2} y+3xy^ {2} +y^ {3} x3 + 3x2y+3xy2 +y3. Question: Suppose there is a blacksmith who made a metal cube with the side length of m inches.
The height of the surface above a point (x, y) is the value of the polynomial for that input (x, y), and the solution is the part of the surface that touches the xy plane. So generally, the solution of a 2-variable polynomial is a curve, not a small set of points.
- 4 min
- Sal Khan,Monterey Institute for Technology and Education
- are there any practice problems?Yes there are practice questions for this: http://www.khanacademy.org/math/algebra/exponent-equations/radical_equations/e/radical_equations
- Has Sal ever checked the answer to a question in a video and found out he did it wrong?Wesim, I think I have seen a couple KA videos where Sal checked his work part way through a video, realized he made an error and went back and fixe...
- What is the difference between (-1^3) and (-1)^3?Although there is no difference in the result, there is a difference in the meaning of the two expressions. One of them (-1^3) says that we have to...
- Will solving a cube root equation get you a extraneous solution?No, cube roots don't give you two solutions by solving them. It is only when you raise it to an even number that it can give you an extraneous solu...
- At 0:39, could he have added the cube root of y to each side instead of subtracting 4 times the cube...Yes, he could have. But then he would have another step to isolate the y. He would have to add the opposite of 5 to both sides (same as subtracting...
- what if the numbers or variables inside the radical aren't the same?You wouldn't be able to solve the equation for a numerical value, but you could express one of the variables in terms of the other one. The only wa...
- wait how did you get -5 , isnt it supposed to be -4 insteadThe original equation says -1(y^1/3). When you subtract 4(y^1/3), you get (-1-4)(y^1/3) = -5(y^1/3).
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May 4, 2023 · In the expression \((x – 2y)^{3}\), \(a = x\) and \(b = 2y\). Now, substitute the value in the \(a – b\) whole cube formula, we get \(\Rightarrow\) \((x – 2y)^{3} = x^{3} – 3(x)^{2}(2y) + 3(x)(2y)^{2} – (2y)^{3}\) \(\Rightarrow\) \((x – 2y)^{3} = x^{3} – 6x^{2}y+12xy^{2} – 8y^{3}\)
- What is the expression of the a minus b whole cube formula, i.e. (a-b)^{3}formula?The expression of \\(a\\) minus \\(b\\) whole cube formula is \\((a-b)^{3}=a^{3}-3ab(a-b)-b^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}\\).
- How to find the (a-b)^{3} formula?To find the formula of \\((a-b)^{3}\\), we will have to multiply \\((a-b)\\) itself by three times, i.e. \\((a-b)(a-b)(a-b)\\).
- How do you use the (a-b)^{3} formula?The \\((a-b)^{3}\\) formula is used to find the cube of a binomial and to factorize the numbers which are trinomials without actually calculating.
- What is the formula of a plus b whole cube?The formula of \\(a\\) plus \\(b\\) whole cube i.e., \\((a+b)^{3}\\) is \\((a+b)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3}\\).
- What is the expansion of a minus b whole cube formula, i.e. (a - b)^{3} formula?The expansion of \\((a-b)^{3}\\) is \\((a-b)^{3}=a^{3}-3ab(a-b)-b^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3}\\).
(x + 2y) 3 = x 3 + 6x 2 y +12xy 2 + 8y 3 Facts about the (a+b)3 Formula The formula (a + b) 3 represents the cube of the sum of two terms, “a” and “b.” (a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3
By the formula of a plus b whole cube (a + b) 3, we know; (a + b) 3 = a 3 + b 3 + 3ab (a + b) Subtracting 3ab (a + b) from both sides, we get; (a + b) 3 – 3ab (a + b) = a 3 + b 3. Taking (a + b) common, we get; (a + b) [ (a + b) 2 – 3ab] = a 3 + b 3. We can write the above expression as;
