Question

(l+m)^2-(l-m)^2- 4lm

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Answer 1

$\Large{\underbrace{\underline{\sf{Understanding\: the\; Question}}}}$

Here in this question, concept of  algeberic identities is used. We are given an algeberic expression and we have to simplify it. We can use different Identities to solve this problem.

So let's do it!!

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Given Expression:

⇒ (l+m)²-(l-m)²-4lm

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Solution:

⇒ (l+m)²-(l-m)²-4lm

Now applying identity:

• (A+B)²=A²+B²+2AB

• (A-B)²=A²+B²-2AB

⇒ [(l)²+(m)²+2(l)(m)]-[(l)²+(m)²-2(m)(l)]-4lm

Now simply it!

⇒ [l²+m²+2lm]-[l²+m²-2lm]-4lm

⇒ l²+m²+2lm-l²-m²+2lm-4lm

Now rearranging similar terms!

⇒ l²-l²+m²-m²+2lm+2lm-4lm

⇒ l²-l²+m²-m²+4lm-4lm

Now all same terms with opposite sign will be cancelled out!

⇒ 0

So the final answer is 0.

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Learn More Algebric Identities!!

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

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Answer 2

um.. hello..!!

well, it's R.S Agarwal..!! ^_^