Expand (y-5)3 by using the identity (a-b)3 = a3 - 3a2b +3ab2-b3
Step 1 : (y-5)3 Here a = y, b=5
Step 2 : (y-5)3 = y3 - 3y2 x 5 + (3y) x 52 - 53(Compare and Substitute y and 5 in the place of a and b ie., a = y, b = 5 )
Step 3 : y3 - 5y2 x 5 + (3y) x 25 - 125
Step 4 : The first term becomes as it is, because there is no change in the value.
Step 5 : The second term becomes -3y2 x 5 = -3 x 5y2 = -15y2 - First multiply the numbers, then we will get 15. 15 is multiplied with y2, we will get -15y2.
Step 6 : The third term is multiplied 3y x 52 = 3 x 5 x 5, here first multiply with numbers 3 x 5 x 5 = 75 and this is multiplied with y, then we will get 75y.
Step 7 : Finally 53 means 5 is multiplied by three times ie., 53= 5 x 5 x 5 = 125
Step 8 : Therefore the answer is y3 - 15y2 + 75y - 125
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