What is Commutative, Associative and Distributive laws in maths?
Commutative laws say we can swap numbers, and you still get the same number when you add, for example, a+b = b+a and same for multiplication. Associative laws say it does not matter how we group the number final value will remain the same, for example, (a+b)+c = (a+b)+c , and same for multiplication Distributive laws say that we can have the same answer while multiplying a number by a group of numbers added together or multiplying them separately and then add them, For example, a x ( b+c) = axb + axc
f(x, y) = sin(xy) + x2 ln(y) Find fyx at (0, π⁄2)
Explanation: fy = xcos(xy) + x2⁄y fyx = cos(xy) – xysin(xy) + 2x⁄y Put (x,y) = (0, π⁄2) = 1
If x3 + y3 = 9 and x + y = 3, then the value of x4+y4 is,
x3+y3 = (x + y) × (x2 − xy + y2) Putting given values of x3+y3 and (x + y) 9 = 3 × ((x+y)2 − 3xy) = 3 × (9 − 3xy) = 27 − 9xy 9xy = 18 xy = 2 x4 + y4 = (x2 + y2)2 - 2x2y2 = (x2 + y2)2 - 2*4 [Putting value of xy] = ((x + y)2 - 2xy)2 - 2*4 [Putting values of (x+y) and xy] = (9 - 4)2 - 2*4 = 17