Evaluate the value of the expression:

$$\frac{0.7^3 + 0.3^3}{0.7^2 - 0.7 imes 0.3 + 0.3^2}$$

Question

Evaluate the value of the expression:

$$\frac{0.7^3 + 0.3^3}{0.7^2 - 0.7 	imes 0.3 + 0.3^2}$$

Accepted Answer

**Solution:**

1. Identify the algebraic identity involved:
   - The expression is of the form:
     $$\frac{a^3 + b^3}{a^2 - ab + b^2}$$
   - Here, $a = 0.7$ and $b = 0.3$.

2. Recall the sum of cubes identity:
   $$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$

3. Substitute the identity into the expression:
   $$\frac{a^3 + b^3}{a^2 - ab + b^2} = \frac{(a + b)(a^2 - ab + b^2)}{a^2 - ab + b^2}$$

4. Cancel the common term $a^2 - ab + b^2$ from numerator and denominator:
   $$= a + b$$

5. Substitute the values:
   $$a + b = 0.7 + 0.3 = 1.0$$

**Answer:** The value of the expression is $1$.

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