Evaluate- 198- 198-102- 10296

Applying the #10;identity a^2 b^2 = ( a + b #10;)( a b) in 198 #10;× 198 102 × 10296 . #10; #10; 198 × 198 102 × 10296 = #10; ...

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Byju's Answer

Standard VIII

Mathematics

Algebraic Identities

Evaluate: 1...

Question

Evaluate: $\frac{198 \times 198 - 102 \times 102}{96}$

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Solution

Applying the identity $a^{2} - b^{2} = (a + b) (a - b)$ in $\frac{198 \times 198 - 102 \times 102}{96}$ .

$\frac{198 \times 198 - 102 \times 102}{96} = \frac{(198 + 102) (198 - 102)}{96}$

$= \frac{300 \times 96}{96}$

$= 300$

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Similar questions

Q. Find the value of :

(i) \frac{6.25 \times 6.25 - 1.75 \times 1.75}{4.5} (i i) \frac{198 \times 198 - 102 \times 102}{96}

Choose the correct answers from the given options .

Q. Find the value of :
(i)

(82)^{2} - (18)^{2}

(ii)

(128)^{2} - (72)^{2}

(iii)

197 \times 203

(iv)

\frac{198 \times 198 - 102 \times 102}{96}

(v)

(14.5 \times 15.3)

(vi)

(8.63)^{2} - (1.37)^{2}

Find the values of
(i) $(82)^{2} - (18)^{2}$
(ii) $(128)^{2} - (72)^{2}$
(iii) $197 \times 203$
(iv) $\frac{198 \times 198 - 102 \times 102}{96}$
(v) $(14.7 \times 15.3)$
(vi) $(8.63)^{2} - (1.37)^{2}$

Simplify the following using the identities:

$(i) \frac{58^{2} - 42^{2}}{16} (i i) 178 \times 178 - 22 \times 22 (i i i) \frac{198 \times 198 - 102 \times 102}{96} (i v) 1.73 \times 1.73 - 0.27 \times 0.27 (v) \frac{8.63 \times 8.63 - 1.37 \times 1.37}{0.726}$

Q. Find the value of:
(i) (82)² − (18)²
(ii) (128)² − (72)²
(iii) 197 × 203
(iv)

\frac{198 \times 198 - 102 \times 102}{96}

(v) (14.7 × 15.3)
(vi) (8.63)² − (1.37)²

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Evaluate: 198×198−102×10296

Applying the identity a2−b2=(a+b)(a−b) in 198×198−102×10296. 198×198−102×10296=(198+102)(198−102)96 =300×9696 =300

Evaluate: $\frac{198 \times 198 - 102 \times 102}{96}$

Applying the identity $a^{2} - b^{2} = (a + b) (a - b)$ in $\frac{198 \times 198 - 102 \times 102}{96}$ .

$\frac{198 \times 198 - 102 \times 102}{96} = \frac{(198 + 102) (198 - 102)}{96}$

$= \frac{300 \times 96}{96}$

$= 300$