Question

16(x+y)² - 25(x-3y)² find the answer​

Answer 1

Answer:

-9x+241y

Step-by-step explanation:

-9x+241y is the correct answer.

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Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\:16 {(x + y)}^{2} - 25 {(x - 3y)}^{2}$

can be rewritten as

$\rm = \: 4 \times 4 {(x + y)}^{2} - 5 \times 5 {(x - 3y)}^{2}$

$\rm = \: {4}^{2} {(x + y)}^{2} - {5}^{2} {(x - 3y)}^{2}$

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {x}^{m} \times {y}^{n} \: = \: {(xy)}^{n} \: }}}$

So, using this Law of radical, we get

$\rm = \: {[4(x + y)]}^{2} - {[5(x - 3y)]}^{2}$

$\rm = \: {(4x + 4y)}^{2} - {(5x - 15y)}^{2}$

We know,

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {x}^{2} - {y}^{2} = (x + y)(x - y) \: }}}$

So, using this identity, we get

$\rm = \: (4x + 4y + 5x - 15y)(4x + 4y - 5x + 15y)$

$\rm = \: (9x - 11y)(19y - x)$

Hence,

$\boxed{ \tt{16 {(x + y)}^{2} - 25 {(x - 3y)}^{2} = (9x - 11y)(19y - x)}}$

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More to know :-

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {(x + y)}^{2} = {x}^{2} + 2xy + {y}^{2} \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {(x - y)}^{2} = {x}^{2} - 2xy + {y}^{2} \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {(x + y)}^{2} + {(x - y)}^{2} = 2( {x}^{2} + {y}^{2}) \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {a}^{m} \times {a}^{n} = {a}^{m + n} \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {a}^{m} \div {a}^{n} = {a}^{m - n} \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {a}^{0} \: = \: 1 \: }}}$

$\red{\rm :\longmapsto\:\boxed{ \tt{ \: {( {a}^{m} )}^{n} \: = \: {a}^{mn} \: }}}$