Solve the following. $\frac{(28.4)^2 - (24.4)^2}{(28.4 - 24.4)} = ?$
Algebraic Simplification Using Difference of Squares
The problem requires simplifying the expression $\frac{(28.4)^2 - (24.4)^2}{(28.4 - 24.4)}$. This can be solved efficiently using the algebraic identity for the difference of squares: $a^2 - b^2 = (a - b)(a + b)$.
Applying the Difference of Squares Formula
Let $a = 28.4$ and $b = 24.4$. Applying the formula to the numerator:
$(28.4)^2 - (24.4)^2 = (28.4 - 24.4)(28.4 + 24.4)$
Simplifying the Expression
Substitute the factored numerator back into the original expression:
$ \frac{(28.4 - 24.4)(28.4 + 24.4)}{(28.4 - 24.4)} $
The term $(28.4 - 24.4)$ appears in both the numerator and the denominator. We can cancel this term:
$ \frac{\cancel{(28.4 - 24.4)}(28.4 + 24.4)}{\cancel{(28.4 - 24.4)}} $
Final Calculation
The expression simplifies to:
$ 28.4 + 24.4 $
Performing the addition:
$ 28.4 + 24.4 = 52.8 $
Therefore, the value of the expression is 52.8.
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Important Questions from Simplification
What will come in the place of the question mark ‘?’ in the following question?
(15 + 24) × 3 ÷ 13 + 18 – 5 = ?
What should come in place of the question mark '?' in the following question?
\n13 × 3 of 5 ÷ 26 = ? + 2.5What should come in place of the question mark '?' in the following question?
10% of 450 - (8 × 5) = ? × 5
What will come in the place of the question mark ‘?’ in the following question?
(66)2 - (34)2 + ?2 = (60)2
What will come in the place of the question mark ‘?’ in the following question?
3 × ? ÷ 9 = ∛729 × √121
