Find (a + b)4 - (a - b)4. Hence, evaluate ( 3 + 2 )^4 - ( 3 - 2 )^4

(a + b)4 = [^4 C_0 a^4 + ^4 C_1 a^3 b + ^4 C_2 a^2 b^2 + ^4 C_3 a b^3 + ^4 C_4 b^4 ] font-family:Tahoma font-size:8px and ; (a-b )^4 ;= ^4 C_0a^4-^4C_1a^3b+^4C_2a^2 b^2 - ^4 C_3 a b^3 + ^4 C_4 b^4 ] font-family:Tahoma font-size:8px l ;(a+b)^4 ;- (a-b )^4 ;= 2 [ ^4C_1a^3b ;+^4C_3ab^3 ] =2 [4a^3b ;+4ab^3 ] ;= ;8ab [a^2+b^2 ] ( 3 ;+ 2 )^4 ;- ; ( 3 ;- 2 )^ 4 ; = ;8. 3. 2 [ ( 3 )^2+ ( 2 )^2 ] = ;8. 3. 2 [3+2 ] ;= ;40. 3. 2 ;= ;40 6

Find (a + b)4 - (a - b)4. Hence, evaluate ( 3 + 2 )^4 - ( 3 - 2 )…

Download App

Question

Find (a + b)⁴ - (a - b)⁴. Hence, evaluate ${(\sqrt 3 + \sqrt 2 )^4} - {(\sqrt 3 - \sqrt 2 )^4}$

✓

Answer

(a + b)⁴ ^{$ = {[^4}{C_0}{a^4}{ + ^4}{C_1}{a^3}b{ + ^4}{C_2}{a^2}{b^2}$${ + ^4}{C_3}a{b^3}{ + ^4}{C_4}{b^4}]$}
$\style{font-family:Tahoma}{\style{font-size:8px}{and\;\left(a-b\right)^4{\;=\lbrack^4}C_0a^4-^4C_1a^3b+^4C_2a^2{b^2}}}$${ - ^4}{C_3}a{b^3}{ + ^4}{C_4}{b^4}]$
$$$\style{font-family:Tahoma}{\style{font-size:8px}{\begin{array}{l}{\therefore\;(a+b)^4\;-\left(a-b\right)^4\;=}2\left[{}^4C_1a^3b\;+^4C_3ab^3\right]\\=2\left[4a^3b\;+4ab^3\right]\;=\;8ab\left[a^2+b^2\right]\\\therefore\left(\sqrt3\;+\sqrt2\right)^4\;-\;\left(\sqrt3\;-\sqrt2\right)^{4\;}=\;8.\sqrt3.\sqrt2\left[\left(\sqrt3\right)^2+\left(\sqrt2\right)^2\right]\\=\;8.\sqrt3.\sqrt2\left[3+2\right]\;=\;40.\sqrt3.\sqrt2\;=\;40\sqrt6\end{array}}}$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "3 Marks Question" from Binomial Theorem→Binomial Theorem — all question types→MATHS STD 11 Science question papers→Rajasthan Board STD 11 Science question papers→Rajasthan Board question paper generator→

Binomial Theorem — MATHS STD 11 Science — Question

Answer

Need a full question paper?

Explore more

Similar questions