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Dividend, Divisor, Quotient, Remainder

Simplify: (i...

Question

Simplify:

(i) $\frac{173 \times 173 \times 173 + 127 \times 127 \times 127}{173 \times 173 - 173 \times 127 + 127 \times 127}$

(ii) $\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}$

(iii) $\frac{1.2 \times 1.2 \times 1.2 - 0.2 \times 0.2 \times 0.2}{1.2 \times 1.2 + 1.2 \times 0.2 + 0.2 \times 0.2}$

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Solution

(i) The given expression is
Assumeand. Then the given expression can be rewritten as
Recall the formula for sum of two cubes
Using the above formula, the expression becomes
Note that both and b are positive. So, neithernor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
(ii) The given expression is
Assumeand. Then the given expression can be rewritten as
Recall the formula for difference of two cubes
Using the above formula, the expression becomes
Note that both, b is positive and unequal. So, neithernor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes
(iii) The given expression is
Assumeand. Then the given expression can be rewritten as
Recall the formula for difference of two cubes
Using the above formula, the expression becomes
Note that both, b is positive and unequal. So, neithernor any factor of it can be zero.
Therefore we can cancel the termfrom both numerator and denominator. Then the expression becomes

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Similar questions

Q. Simplify:

(i)

\frac{173 \times 173 \times 173 + 127 \times 127 \times 127}{173 \times 173 - 173 \times 127 + 127 \times 127}

\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}

\frac{1.2 \times 1.2 \times 1.2 - 0.2 \times 0.2 \times 0.2}{1.2 \times 1.2 + 1.2 \times 0.2 + 0.2 \times 0.2}

Q. Using algebraic identity evaluate :

\frac{173 \times 173 \times \times 173 + 127 \times 127 \times 127}{173 \times 173 - 173 \times 127 + 127 \times 127}

\frac{155 \times 155 \times 155 - 55 \times 55 \times 55}{155 \times 155 + 155 \times 55 + 55 \times 55}

Subtract $15 \frac{5}{3}$ from $17 \frac{3}{2}$

If you subtract $15 \frac{5}{3}$ from $17 \frac{3}{2}$ , you will get

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