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The equation solver allows you to enter your problem and solve the equation to see the result. Solve in one variable or many.
Explanation: # (x-y)^3= (x-y) (x-y) (x-y)#. Expand the first two brackets: # (x-y) (x-y)=x^2-xy-xy+y^2#. #rArr x^2+y^2-2xy#. Multiply the result by the last two brackets: # (x^2+y^2-2xy) (x-y)=x^3-x^2y+xy^2-y^3-2x^2y+2xy^2#. #rArr x^3-y^3-3x^2y+3xy^2#.
Answer: The expansion of (x-y) 3 is x 3 - y 3 - 3x 2 y + 3xy 2. Let us see how to expand (x-y) 3. Explanation: The expression (x-y) 3 can be written as, (x-y)(x-y)(x-y) First simplify (x-y)(x-y) by binomial multiplication. (x-y)(x-y) = x 2 - 2xy + y 2. Now multiply (x-y) with x 2 - 2xy + y 2 (x-y)(x-y)(x-y) = (x-y)(x 2 - 2xy + y 2) = x 3 - 2x 2 ...
Each number in Pascal's triangle is the sum of the 2 digits just above it, to the right & left. Or you could just multiply the 3 factors together (x+y) (x+y) (x+y) = (x^2+2y+y^2) (x+y)= (x^3+3x^2y+3xy^2+y^3) Or you might just remember the formula: (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 and replace a with x and b with y.
The calculator provides detailed step-by-step solutions, aiding in understanding the underlying concepts. To solve an algebraic expression, simplify the expression by combining like terms, isolate the variable on one side of the equation by using inverse operations.
The perfect cube forms (x+y)^3 (x +y)3 and ( x-y)^3 (x−y)3 come up a lot in algebra. We will go over how to expand them in the examples below, but you should also take some time to store these forms in memory, since you'll see them often:
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