The correct option is B 100 We need to find value of (58)^2 (42)^216 We know, a^2 b^2 = (a+b)(a b) #160; #160; #160; (∵ Identi ...

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Applying Difference of Squares as a Product of Its Sum and Difference

582 - 42216 =...

Question

$\frac{58^{2} - 42^{2}}{16} =$ _______.

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100

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Solution

The correct option is B $100$
We need to find value of $\frac{(58)^{2} - (42)^{2}}{16}$
We know, $a^{2} - b^{2} = (a + b) (a - b)$ $(∵ Identity)$
Here $a = 58$ and $b = 42$
Thus $(58)^{2} - (42)^{2} = (58 + 42) (58 - 42)$
$= (100) (16)$
$= 1600$
$\Rightarrow \frac{(58)^{2}) - (42)^{2})}{16} = \frac{1600}{16}$
$= 100$

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Similar questions

Q. Simplify:

\frac{58^{2} - 42^{2}}{16}

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. Write the following decimal fractions as decimal numbers:

\frac{422}{100}

Q. Draw a histogram to represent the following data set.

Marks	$0 - 10$	$10 - 20$	$20 - 40$	$40 - 50$	$50 - 60$	$60 - 70$	$70 - 90$	$90 - 100$
No. of students	$4$	$6$	$14$	$16$	$14$	$8$	$16$	$5$

Q. If 422 + 630 = 1052 , then 630 + 422 =

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582−42216= _______.

The correct option is B 100We need to find value of (58)2−(42)216We know, a2−b2=(a+b)(a−b) (∵ Identity)Here a=58 and b=42Thus (58)2−(42)2=(58+42)(58−42)=(100)(16)=1600⇒(58)2)−(42)2)16=160016=100

$\frac{58^{2} - 42^{2}}{16} =$ _______.