Question

factorise x^2-4xy+4y^2

Answer 1

ANSWER
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The given polynomial can be factorized into two different ways : -

1) By using the formula ( a + b )²

2) By splitting the middle term into two terms such that

✓ The sum of the two middle terms would be -4xy

✓ Their product would be 4x²y²

BY FORMULA 1 : -
********************
{ ( a - b )² = a² - 2ab + b² }


x² - 4xy + 4y²

=> x( x ) - 2( x )( 4y ) + 2y( 2y )

=> ( x + 2y ) ( x + 2y ) or ( x + 2y )² ANS

BY FORMULA 2 : -
*********************

x² - 4xy + 4y²

=> x² - 2xy - 2xy + 4y²

=> x ( x - 2y ) - 2y ( x - 2y )

=> ( x - 2y ) ( x - 2 ) ANS

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#BE BRAINLY

Answer 2

Answer:

After factorizing the given equation we get ( x - 2y )².

Step-by-step explanation:

Step 1:- First we have to write the equation

⇒ x² - 4xy + 4y²

Step 2:- Now,

we can write 4y² like ( 2²y² ),

⇒ 4y² = 2²y²

          = ( 2y )²

even we can write 4xy like ( 2 × x × 2y )

⇒ 4xy = ( 2 × x × 2y )

Now the equation will be

⇒ x² - 2 × x × 2y + ( 2y )²

Step 3:- we will apply Perfect Square Formula, we get

⇒ x² - 2 × x × 2y + ( 2y )² = ( x - 2y )²    [ a² - 2ab + b² = ( a - b )² ]

∴ After factorizing, we get ( x - 2y )².

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