Question

LETS TEST YOUR BRAIN
I WANT THE CORRECT ANSWER GUYS LETS SEE WHO WILL SOLVE THIS HARD QUESTION

Answer 1

Answer :-

• $\bigstar \rm \: { \bf 288xy \:} is \: the \: answer$

Step-by-step-Explaination :-

Given & Find :-

$\sf Simplify : - \: (8x + 9y)^{2} - (8x - 9y) ^{2}$

Solution :-

$\sf \: (8x + 9y)^{2} - (8x - 9y) ^{2}$

To solve this we need to know a Identities of it :-

$\: \boxed{ \sf(a + b) ^{2} - (a - b) ^{2} = 4ab \: \bigstar}$

So , Let us Assume that ,

$\sf(a + b) ^{2} = (8x + 9y)^{2}$

$\sf \: (a - b) ^{2} = (8x - 9y) ^{2}$

Also we can say that :-

$\sf \: a = 8x$

$\sf \: b = 9y$

Hence , also we can mention :

$\sf {a}^{2} = {8x}^{2}$

$\sf {b}^{2} = {9y}^{2}$

So, let's solve :

$\sf \: (8x + 9y)^{2} - (8x - 9y) ^{2}$

$: : = \sf 4(8x\times9y)$

$: : = \sf 4\times72xy$

$: : = \sf\bf\underline { 288xy} \bigstar$

$\sf\bigstar \underline {\underline{ \: Additional \: information}}$

$1.) \: \sf {a}^{2} - {b}^{2} = (a + b)(a - b)$

$2.) \: \sf ({a} + {b} ) ^{2} = {a}^{2} + 2ab + {b}^{2}$

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

$4.) \: \sf {a} ^{2} - {b} ^{2} = ( {a + b})^{2} - 2ab$

$5.) \: \sf {a} ^{2} + {b} ^{2} = ( {a - b})^{2} + 2ab$

$6.) \: \sf ({a} + {b}) ^{2} = ( {a - b})^{2} + 4ab$

$7.) \: \sf ({a} - {b}) ^{2} = ( {a + b})^{2} - 4ab$

$8.) \: \sf ({a} + {b}) ^{2} = ( {a - b})^{2} + 4ab$

$9.) \: \sf (4{a} {b}) = ( {a + b})^{2} - (a - b) ^{2}$

$10.) \: \sf \: a b = ( \dfrac{a + b}{2} ) ^{2} \: \: - ( \dfrac{a - b}{2} ) ^{2}$

$11.) \: \sf ({a} + {b} + c) ^{2} = {a}^{2} + {b }^{2} + {c}^{2} + 2ab + 2bc + 2ca$

$\:12.) { \sf(a + b) ^{2} - (a - b) ^{2} = (a) ^{2} -( b)^{2} \: }$

$\:13.) { \sf(a + b) ^{2} + (a - b) ^{2} =2 (a +b)^{2} \: }$

$\:14.) \sf \:If (a + b+c)= 0 \: Then , a^3+b^3+c^3 = 3abc$

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