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How do you do the following divisions and find quotient and remainder a3-b3 by a-b?
Wiki User
∙ 12y ago
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Elroy Murazik
Wiki User
∙ 12y agoYou can use the remainder theorem to show that the remainder on division is 0. If you substitute a = b in a3 - b3 the value is 0. Therefore (a-b) is a factor of a3 - b3 and so the remainder is 0.
To find the quotient, you do the division like you'd do a long division with numbers. It is a bit difficult to work with this browser, but here goes:
a goes into a3: a2 times so the first term of the quotient is a2.
Now a2*(a-b) = a3 - a2b
Subtract this expression from a3 - b3
So the remainder, at this stage, is a2b - b3
Now a goes into a2b: ab times so the next term of the quotient is ab.
ab*(a-b) = a2b - ab2
Subtract this from the last remainder to give the new remainder of ab2 - b3
A goes into ab2: b2 times so the next term of the quotient is b2.
b2*(a-b) = ab2 - b3
Subtract this from the previous remainder to give the next remainder of 0.
Done.
So, a3 - b3 = (a - b)*(a2 + ab + b2)
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What is the formula for multiplying a3 b3?
a3*b3 = a3b3
What is the LCM of a2b5 plus a3b3?
LCM(a2b5, a3b3) The LCM of both numbers HAS to have the largest coefficient of both variables. For a, it's a3, and for b it is b5. So the LCM is a3b5.
What is cross-product and dot-product?
Cross products and dot products are two operations that can be done on a pair of 2-dimensional, 3-dimensional, or n-dimensional vectors. Both can be viewed in terms of mathematics or their physical representations.The dot product of two three-dimensional vectors A= and B= is a1b1+ a2b2 + a3b3. The definition in high dimensions is completely analogous. Notice that the dot product of two vectors is a scalar, not a vector. The dot product also equals |A|*|B|cosθ, where |A| and |B| are the magnitudes of A and B, respectively and θ is the angle between the vectors. This is the same as saying that the dot product is the magnitude of one vector multiplied times the component of the second vector that is parallel to the first. Notice that this means that the dot product of two vectors is 0 if and only if they are perpendicular.The cross product is a little more complicated. In three dimensions, A × B = . Notice that this operation results in another vector. This vector always points in a direction perpendicular to both A and B, and this direction can be determined by the right-hand rule. Physically, the magnitude of this vector equals |A|*|B|sinθ, or the magnitude of the first vector times the component of the other that is perpendicular to the first. So the cross product is 0 when the vectors are parallel.
