Question

evaluate each of the following using appropriate identities :-

1) (2x - 3y)cube
2)(2x +1/3)cube
3)if a=b = 5 and ab = 6,find a square +b square

Answer 1

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Here's your answer...

1) The identity used here is...
(a-b)³ = a³-b³-3ab(a-b)
(2x-3y)³ = (2x)³-(3y)³-3×2x×3y×(2x-3y)
= 8x³-27y³-18xy(2x-3y)
= 8x³-27y³-36x²y+54xy²

2) The identity used here is...
(a+b)³ = a³+b³+3ab(a+b)
(2x+⅓)³ = (2x)³ + (⅓)³ + 3×2x×⅓(2x+⅓)
= 8x³ + 1/27 + 2x(2x+⅓)
= 8x³ + 1/27 + 4x² + ⅔x

3) The identity used here is...
(a+b)² = a²+b²+2ab
a+b = 5
ab = 6
5² = a²+b²+2×6
25 = a²+b²+12
a²+b² = 13

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