First, look at the given problem. eg. (8n-3)^3. Mark the first term (8n) A then mark the second term (-3) B. Do this formula. (a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3
Consider a binomial (a+b). The cube of the binomial is given as =(a+b)3 =a3 + 3a2b + 3ab2 + b3.
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To calculate the cube of a binomial, you can multiply the binomial with itself first (to get the square), then multiply the square with the original binomial (to get the cube). Since cubing a binomial is quite common, you can also use the formula: (a+b)3 = a3 + 3a2b + 3ab2 + b3 ... replacing "a" and "b" by the parts of your binomial, and doing the calculations (raising to the third power, for example).
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that;s so simple . try it
(a + b)3 = a3 + 3a2b + 3ab2 + b3
The cube of a binomial is the cube of two terms separated by an addition or subtraction sign, such as (2a + 3b) or (ab - cd).For example, (2x - 5y)3 = 8x3 - 40x2y + 50xy2 - 20x2y + 100xy2 - 125y3.The detailed method of expanding this binomial is : (2x - 5y)3 = (2x - 5y)(2x - 5y)(2x - 5y) = (4x2 - 20xy + 25y2)(2x - 5y) = 8x3 - 40x2y + 50xy2 - 20x2y + 100xy2 - 125y3
The cube of the binomial ( (4k - 7q) ) can be calculated using the formula for the cube of a binomial, which is ( (a - b)^3 = a^3 - 3a^2b + 3ab^2 - b^3 ). Here, ( a = 4k ) and ( b = 7q ). Applying the formula, we get: [ (4k - 7q)^3 = (4k)^3 - 3(4k)^2(7q) + 3(4k)(7q)^2 - (7q)^3. ] This simplifies to: [ 64k^3 - 84k^2q + 147kq^2 - 343q^3. ]
The cube of a binomial refers to the expression ((a + b)^3) and can be expanded using the binomial theorem. It is defined as ( (a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3 ). This expansion includes the sum of the cubes of the individual terms and three times the products of the squares of each term with the other term. The formula can also be applied to ((a - b)^3), yielding a similar structure with alternating signs.
The special products include: difference of the two same terms square of a binomial cube of a binomial square of a multinomial (a+b) (a^2-ab+b^2) (a-b) (a^2+ab+b^2)
The special products include: difference of the two same terms square of a binomial cube of a binomial square of a multinomial (a+b) (a^2-ab+b^2) (a-b) (a^2+ab+b^2)