Question

how to do step by step factorise (l+m)^2-4lm

Answer 1

Step by step solution :

Step 1 :

1.1 Evaluate : (l+m)2 = l2+2lm+m2
Trying to factor a multi variable polynomial :

1.2 Factoring l2 - 2lm + m2

Try to factor this multi-variable trinomial using trial and error

Found a factorization : (l - m)•(l - m)

Detecting a perfect square :

1.3 l2 -2lm +m2 is a perfect square

It factors into (l-m)•(l-m)
which is another way of writing (l-m)2

How to recognize a perfect square trinomial:

• It has three terms

• Two of its terms are perfect squares themselves

• The remaining term is twice the product of the square roots of the other two terms

Answer 2

Solution ●●●●
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$= {l}^{2} + 2.l.m + {m}^{2} - 4lm \\ \\ = {l}^{2} + 2lm + {m}^{2} - 4lm$

$= {l}^{2} - 2lm + {m}^{2} \\ \\ = {(l - m)}^{2} \\ \\ = (l - m)(l - m)$
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I hope it will help you