Simplify
​$$\frac{(4.2)^3-(1.2)³}{(4.2)^2+5.04+(1.2)^2 }$$​​

Correct option is B

Given:
​$$\frac{(4.2)^3-(1.2)³}{(4.2)^2+5.04+(1.2)^2 }$$​​
Formula Used:

​$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)\\\\$$ 

Solution:

By using the above identity:

$$\frac{(4.2)^3-(1.2)³}{(4.2)^2+5.04+(1.2)^2 }\\\implies \frac{(4.2-1.2)[4.2^2+4.2 \times 1.2+1.2^2]}{4.2^2+5.04+1.2^2 }\\\implies \frac{(3)[4.2^2+ 5.04+1.2^2]}{4.2^2+5.04+1.2^2 }\\\implies 3$$​

Information Booster:

​$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)\\\\(a - b)^3 = a^3 - b^3 - 3ab(a - b)\\(a + b)^3 = a^3 + b^3 + 3ab(a + b)\\$$​​

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