Question

Evaluate : 307*293
:4.15*3.85

Answer 1

$\bold{Hey\: Mate \:Here \:Is\: Your\: Answer...}$

Q 1 ) Evaluate 307 × 293

$\large{\underline{\bold{{Solution...}}}$

Now According To Question We Need To Evaluate 307 × 293

So Now We Can Write

$\bold{307 \:As \:300\: + \:7}$

Similarly

We Can Write

$\bold{293\: As \:300 \:- \:7}$

So Now Using This Form Instead Of 307 × 293 We Have

$\boxed{\bold{(300 + 7) (300 - 7 )}}$

Therefore Now We Know An Identity That Is ...

$\boxed{\bold{( a + b ) ( a - b ) = {a}^{2}\:-\: {b}^{2} \:}}$

Here

$\bold{\: a\: = \:300\: \;And \;\: b\: =\: 7 }$

So We Have ...

$\bold{(300 + 7)(300 - 7) = {300}^{2} - {7}^{2}}$

That Is ...

$\bold{307 \times 293 = 90000 - 49}$

That Is ...

$\bold{300 \times 293 = 89951}$

$\bold{So \:We\: Have \:Answer \:For \:Question\: 1\: Equal\: To\: ...}$

$\boxed{\bold{89951}}$

Now Let's Move To Second Question ..

Q 2 ) Evaluate 4.15 × 3.85

So Now In This Question We Can Use Same Logic That Is ....

We Can Write

$\bold{4.15 \;\:As\;\; 4.00 \:+ \:0.15}$

And

$\bold{3.85 \:\:As \:\;4.00 - 0.15 }$

So Now Putting This Form Of Numbers In Question We Have ....

$\bold{(4.00\: + \:0.15)(4.00-0.15 )}$

Now By Using The Same Identity That We Used Above Where

$\bold{a\: =\: 4 \:And\:b\: =\: 0.15}$

We Have ...

$\bold{(4.00\: +\:0.15)(4.00 \:- \:0.15)\:=\: {4.00}^{2} - {0.15}^{2} }$

That Is ..

$\bold{4.15 \times 3.85 = 16 - \: 0.0225}$

That Is ..

$\bold{4.15 + \times 3.85 = 15.9775}$

Therefore Answer For Second Question Is ...

$\boxed{\bold{15.9775}}$

Hence The Required Answers Are

$\boxed{\bold{89951\: \;And\:\;15.9775}}$

$\large{\bold{Thanks..}}$