Question 3: Using suitable identity evaluate the following:

(i) 98^{3}

(ii) 188 × 212

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(98)^{3} = (100 - 2)^{3}

(100 - 2)^{3} is of the form (a - b)^{3}

(a - b)^{3} = a^{3} - 3a^{2}b + 3ab^{2} - b^{3}

So, (100 - 2)^{3} = 100^{3} - 3 × 100^{2} × 2 + 3 × 100 × 2^{2} - 2^{3}

= 1,000,000 - 60,000 + 1200 - 8 = **9,41,192**

188 × 212 = (200 - 12)(200 + 12)

The expression is of the form (a - b)(a + b)

(a - b)(a + b) = a^{2} - b^{2}

So, (200 - 12)(200 + 12) = 200^{2} - 12^{2}

= 40,000 - 144 = **39856**

Class 9 Maths

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