Question

simplify (6ab-3ab)^3​

Answer 1

Answer:

27(ab)^3

Step-by-step explanation:

(6ab-3ab)^3

=(3ab)^3

=3^3×a^3×b^3

=27(ab)^3

Answer 2

$\huge\bold{\gray{\sf{Answer:}}}$

Explanation:

Here ,this identity is used:

$\bold{\boxed{\purple{{(x - y)}^{3} = {x}^{3} + {y}^{3} -3 {x}^{2} y + 3 x{y}^{2} }}}$

${(6ab - 3ab)}^{3} = {(6ab)}^{3} - {(3ab)}^{3} - 3( {6ab)}^{2} (3ab) + 3(6ab) {(3ab)}^{2}$

$= > 216 {a}^{3} {b}^{3} - 27 {a}^{3} {b}^{3} - 3[36 {a}^{2} {b}^{2} (3ab)]+ 3[(6ab)(9 {a}^{2} {b}^{2} )]$

$= > 216 {a}^{3} {b}^{ 3} - 27 {a}^{3} {b}^{3} - 3[108 {a}^{3} {b}^{3} ]+ 3[54 {a}^{3} {b}^{3} ]$

$= > 216 {a}^{3} {b}^{3} - 27 {a}^{3} {b}^{3} - 324 {a}^{3} {b}^{3} + 162 {a}^{3} {b}^{3}$

$= > 189 {a}^{3} {b}^{3} - 324 {a}^{3} {b}^{3} + 162 {a}^{3} {b}^{3}$

$= > - 135 {a}^{3} {b}^{3} + 162 {a}^{3} {b}^{3}$

$= > 27 {a}^{3} {b}^{3} = > {(3ab)}^{3}$

$\bold\fcolorbox{aqua}{orange}{Answer}$$\bold{27 {a}^{3} {b}^{3} = {(3ab)}^{3}}$

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Other Identity related to this :

$\bold{\boxed{ {(x -y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

$\bold{\boxed{ {x}^{3} + {y}^{3} = {x}^{3} + {y}^{3} + 3xy(x + y)}}$

$\bold{\boxed{(x + y)(x + z) = {x}^{2} + (y+ z)x + yz}}$

$\bold{\boxed{ {(x +y)}^{3} = {x}^{3} + {y}^{3} +3xy[x+y]}}$