Question

pls help I'll mark brainliest​

Answer 1

Answer:

$\large\bold\red { - 32(3 {x}^{2} + 8)}$

Step-by-step explanation:

We have to simplify,

${(2x - 4)}^{3} - {(2x + 4)}^{3}$

Now,

We know that,

$\bold \purple{{a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) }$

Therefore,

We get,

$= (2x - 4 - 2x - 4)( {(2x - 4)}^{2} + (2x - 4)(2x + 4) + {(2x + 4)}^{2} ) \\ \\ = - 8( {(2x)}^{2} + {(4)}^{2} - 16x + {(2x)}^{2} - {(4)}^{2} + {(2x)}^{2} + {(4)}^{2} + 16x)) \\ \\ = - 8(4 {x}^{2} + 16 + 4 {x}^{2} - 16 + 4 {x}^{2} + 16) \\ \\ = - 8(12 {x}^{2} + 32) \\ \\ = \bold { - 32(3 {x}^{2} + 8)}$

Answer 2

Solution :

$\hookrightarrow{(2x - 4)}^{3} - {(2x + 4)}^{3} \\ \\ \hookrightarrow \bigg((2x - 4 )- (2x + 4) \bigg) \bigg ( {(2x - 4)}^{2} + (2x - 4)(2x + 4) + {(2x + 4)}^{2} \bigg) \\ \\ \hookrightarrow 2x - 4 - 2x - 4 \bigg ( {(2x)}^{2} + {(4)}^{2} - 2(2x)(4) + {(2x)}^{2} - {(4)}^{2} + {(2x)}^{2} + {(4)}^{2} + 2(2x)(4) \bigg )\\ \\ \hookrightarrow - 8 \bigg( 3 {(2x)}^{2} + {(4)}^{2} \bigg) \\ \\ \hookrightarrow - 8 \bigg(12 {x}^{2} + 16 \bigg) \\ \\ \hookrightarrow - 96 {x}^{2} + 128 \\ \\ \hookrightarrow- 32(3 {x}^{2} + 4)$

Therefore , the final answer is -32(3x² + 4)

Identities used :

$\sf \star \: \: {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} ) \\ \\ \sf \star \: \: (a - b)(a + b) = {a}^{2} - {b}^{2} \\ \\ \sf \star \: \: {(a + b)}^{2} = {(a)}^{2} + {(b)}^{2} + 2ab \\ \\ \sf \star \: \: {(a - b)}^{2} = {(a)}^{2} + {(b)}^{2} - 2ab$