Question

Solve the question given in the picture....
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Answer 1

$\huge{\underline{\underline{Answer\::-}}}$

>> Given to multiply



$(a+b )^2 × (a - b )^2$





>>As we know that



$(a+b)^2 = a^2 + 2ab + b^2$

and
$(a - b)^2 = a^2 - 2ab + b^2$





>>Then by multiplying



= $(a^2 + 2ab + b^2 ) × (a^2 - 2ab + b^2)$



$= a^2 (a^2 - 2ab + b^2) \\ + 2ab (a^2 - 2ab + b^2) \\ + b^2 (a^2 - 2ab + b^2)$



$= (a^4 - 2a^3b + a^2b^2 ) \\+ (2a^3b - 4a^2b^2 + 2ab^3 ) \\ + ( b^4 - 2ab^3 + a^2b^2)$



$= a^4 + b^4 - 2a^2b^2$

Hope it helps you

Answer 2

Answer:

$\mathsf{(a+b)^2\times (a-b)^2}\\\\\implies \mathsf{[(a+b)(a-b)]^2}\\\\\implies \mathsf{(a^2-b^2)^2}\\\\\implies \mathsf{a^4+b^4-2a^2b^2}$

Step-by-step explanation:

We know that by laws of indices :

a² × b²

⇒ ( ab )²

We also know that by expansion :

( a + b )( a - b ) = a² - b²

Finally the expansion :

( a - b )² = a² + b² - 2 ab is used .

The expression ( a - b)²

⇒ ( a - b)( a - b )

⇒ a ( a - b ) - b ( a - b )

⇒ a²- ab - ab + b²

⇒ a² + b² - 2 ab