Question

Find the area of square whose side is 9ab ²-7b²​

Answer 1

Given :-  

• Side of square is 9ab²  - 7b²  

To Find :-  

• Area of the square  

Solution :-  

~ Here , the concept of Area of Square can be used. As we can see that , we are given side of the square. Then , we can easily find the area by applying the formula of finding area of a square . And we’re given a variable as a value of side , we can use suitable identities to simplify .  

 As we know that ,

• Area of a square = ( Side )²  

By putting the values

= ( 9ab² – 7b² )²

Identity used ::  

( a – b )² = a² + b² + 2ab  

______________________  

= ( 9ab² )² + ( 7b² )² + ( 2 × 9ab² × 7b² )  

= 81a²b⁴−126ab⁴+49b⁴

______________________

Therefore ,  

Area of the square is  81a²b⁴− 126ab⁴+49b⁴

Answer 2

AnswEr-:

• $\red{\mathrm {\underline {\star{ The\:area\:of\:Square \:is \:81a^{2}b^{4} + 49b^{4} - 126ab^{4}\:sq.units}}}}$

Explanation-:

$\mathrm {\bf{ Given-:}}$

• The Side of Square is 9ab ²-7b² units .

$\mathrm {\bf{ To\:Find-:}}$

• The area of Square.

$\mathrm {\bf{\dag{ Solution \;of\:Question-:}}}$

• $\underbrace {\mathrm {\bf{ Understanding \:the\:Concept \:-:}}}$

• We have to find the area of Square whose Side is given .

• By Putting the given Values [ Side ] in the Formula for Area of Square.

• By Doing this We can get the area of Square.

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$\underline{\mathrm {\bf{\dag{ Finding \:Area\;of\:Square-:}}}}$

As, We know that ,

• $\underline{\boxed{\star{\sf{\red{Area_{(Square)}  \: = \: side \times side\:sq.units }}}}}$

$\mathrm {\bf{ Here-:}}$

• The Side of Square is 9ab ²-7b² units .

Now , By Putting known Values in Formula for Area of Square-:

• $\longmapsto {\mathrm { Area \:-: 9ab^{2} -7b^{2} \times 9ab^{2} -7b²^{2} }}$

• $\longmapsto {\mathrm { Area \:-: (9ab^{2} -7b^{2})^{2} }}$

As , We know that Algebraic identities-:

• $\mathrm {\underline {\star{ (a -b)^{2} = a^{2} + b^{2} - 2 ab}}}$

By using this -:

• $\longmapsto {\mathrm { Area \:-: (9ab^{2})^{2} + (7b^{2})^{2} - 2 \times 9ab^ {2} \times 7b^{2} }}$

• $\longmapsto {\mathrm { Area \:-: 81a^{2}b^{4} + 49b^{4} - 18ab^ {2} \times 7b^{2} }}$

• $\qquad \quad \qquad \pink{\underline{\boxed {\frak { Area \:-: 81a^{2}b^{4} + 49b^{4} - 126ab^{4}\:sq.units }}}}$

Hence ,

• $\red{\mathrm {\underline {\star{ The\:area\:of\:Square \:is \:81a^{2}b^{4} + 49b^{4} - 126ab^{4}\:sq.units}}}}$

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