Calculating the Difference of Cubes: $27^3 - 22^3$
To find the value of $27^3 - 22^3$, we can use the algebraic identity for the difference of cubes: $a^3 - b^3 = (a - b)(a^2 + ab + b^2)$
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Identify $a$ and $b$:
- $a = 27$
- $b = 22$
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Calculate the difference $(a - b)$:
$27 - 22 = 5$
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Calculate the terms $a^2$, $ab$, and $b^2$:
- $a^2 = 27^2 = 729$
- $ab = 27 \times 22 = 594$
- $b^2 = 22^2 = 484$
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Calculate the sum $(a^2 + ab + b^2)$:
$729 + 594 + 484 = 1807$
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Multiply the results from step 2 and step 4:
$5 \times 1807 = 9035$
Alternatively, calculate the cubes directly:
- $27^3 = 19683$
- $22^3 = 10648$
- $27^3 - 22^3 = 19683 - 10648 = 9035$
Therefore, the value of $27^3 - 22^3$ is $9035$.
Important Questions from Simplification (Notes)
- In the Delhi zoo, there are some ducks and rabbits. If the heads are counted there are 160, while the legs are 450. What will be number of ducks in the zoo ?
Identify the number that will replace the question mark in the second equation based on the relationship represented in the first equation.
What value should come in the place of question mark (?) in the following equation?
$(0.008\div?) + (0.006 \div 0.03) + (0.008 \div 0.04) =0.5$If 'I' stands for '+', 'J' stands for 'x', 'K' stands for '÷', and 'L' stands for '-', then what will come in place of the question mark (?) in the following equation?
6 K 2 J 4 L 3 I 9 = ?If 'A' stands for '$\div $', 'B' stands for 'x', 'C' stands for '+' and 'D' stands for '-', then what will come in place of the question mark (?) in the following equation?
33 A 3 C 4 B 2 D 4 A 2 = ?
