Math, asked by eshan13, 1 year ago

Answer fast for 100 points!!!! $$
 ({58}^{2}  -  {42}^{2} ) \div 16
Simply it using the identities....

Answers

Answered by Anonymous
13

\mathfrak{Answer:}

= 100.

\mathfrak{Step-by-Step\;Explanation:}

\bold{(58^2-42^2)\div 16}\\\\\\\bigstar\quad\textbf{We know that : \boxed{\bold{a^2-b^2=(a+b)(a-b)}}}\\\\\\\bold{=(58+42)(58-42)\div 16}\\\\\\\bold{=100\times16\times\dfrac{1}{16}}\\\\\\\bold{=100.}

Important Formulae :

1. a² – b² = (a – b)(a + b)

2.(a+b)² = a² + 2ab + b²

3.a² + b² = (a – b)² + 2ab

4.(a – b)² = a² – 2ab + b²

5.(a + b + c)² = a² + b² + c² + 2ab + 2ac + 2bc

6.(a – b – c)² = a² + b² + c² – 2ab – 2ac + 2bc

7.(a + b)³ = a³ + 3a²b + 3ab² + b³

8.(a + b)³ = a³ + b³ + 3ab(a + b)

9.(a – b)³ = a³ – 3a²b + 3ab² – b³

10.a³ – b³ = (a – b)(a² + ab + b²)

11.a³ + b³ = (a + b)(a² – ab + b²)

12.(a + b)³ = a³ + 3a²b + 3ab² + b³

Answered by pratyush4211
4

\underline{\textbf{\huge{Question}}}

\mathbf{ ({58}^{2} - {42}^{2} ) \div 16}

\underline{\textbf{\huge{Answer}}}

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

According To Identity.

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

Using This Identity

Numerator=58²-42²

Can Written as

 \implies\mathbf{(58 + 42)(58 - 42)} \\  \\ \implies  \mathbf{100 \times 16}

Numerator=100×16

Fraction

 \implies\mathbf{ \frac{100 \times \cancel{ 16}}{ \cancel{16}}} \\  \\   \implies \mathbf{100}

CHECK

58²=3364

42²=1764

When Divided by 16

 \implies\mathbf{ \frac{3364 - 1764}{16}}  \\  \\  \implies \mathbf{ \frac{ \cancel{16}00}{ \cancel{16}}}  \\  \\  \implies \mathbf{100}

Hence It is Right

\boxed{\mathbf{\huge{Answer=100}}}

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