The simplification of frac{0.67 times 0.67 ti | vedclass

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(A) Let $a = 0.67$ and $b = 0.1$.Then $a^3 = 0.67 	imes 0.67 	imes 0.67$ and $b^3 = 0.1 	imes 0.1 	imes 0.1 = 0.001$.Also,$ab = 0.67 	imes 0.1 =

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$0.57$

Vedclass · Answer

(A) Let $a = 0.67$ and $b = 0.1$.Then $a^3 = 0.67 	imes 0.67 	imes 0.67$ and $b^3 = 0.1 	imes 0.1 	imes 0.1 = 0.001$.Also,$ab = 0.67 	imes 0.1 = 0.067$ and $b^2 = 0.1 	imes 0.1 = 0.01$.The expression is of the form $\frac{a^3 - b^3}{a^2 + ab + b^2}$.Using the algebraic identity $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$,the expression simplifies to:$\frac{(a - b)(a^2 + ab + b^2)}{a^2 + ab + b^2} = a - b$.Substituting the values,we get $0.67 - 0.1 = 0.57$.

The simplification of $\frac{0.67 \times 0.67 \times 0.67 - 0.001}{0.67 \times 0.67 + 0.067 + 0.01}$ gives

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