Simplify ((0.5)^3 + (0.3)^3)/((0.5)^2 - 0.5 × 0.3 + (0.3)^2).

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Simplification & Approximation · Question 52 of 71

Question 52

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Simplify $\dfrac{(0.5)^3 + (0.3)^3}{(0.5)^2 - 0.5 \times 0.3 + (0.3)^2}$ .

0.08Correct answerYour answer0.2Correct answerYour answer0.34Correct answerYour answer0.8Correct answerYour answer

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CorrectNot quiteAnswer D

Correct answer: D

This is $\frac{a^3 + b^3}{a^2 - ab + b^2}$ with $a = 0.5$ , $b = 0.3$ .
Since $a^3 + b^3 = (a + b)(a^2 - ab + b^2)$ , the fraction equals $a + b$ .
$0.5 + 0.3 = 0.8$ .

Worth noting

Direct check: numerator $0.125 + 0.027 = 0.152$ , denominator $0.25 - 0.15 + 0.09 = 0.19$ , and $0.152 \div 0.19 = 0.8$ . Using $a - b$ gives 0.2; 0.34 is the denominator with the middle term dropped.

Concept: Using a³ + b³ = (a + b)(a² − ab + b²)
Typical timeTypical: 60 s
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Simplify (0.5)3+(0.3)3(0.5)2−0.5×0.3+(0.3)2\dfrac{(0.5)^3 + (0.3)^3}{(0.5)^2 - 0.5 \times 0.3 + (0.3)^2}(0.5)2−0.5×0.3+(0.3)2(0.5)3+(0.3)3​.

Explanation

Simplify $\dfrac{(0.5)^3 + (0.3)^3}{(0.5)^2 - 0.5 \times 0.3 + (0.3)^2}$ .