Question

Factorise the following.
(1) 9x^2 - 12xy + 4y^2 .
(2) 1 - 2x + x^2 .
(3) 16x^2 - 40xy + 25y^2. ​

Answer 1

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1) Rewrite 9x2 as (3x)2.

(3x)2+12xy+4y2

Rewrite 4y2 as (2y)2.

(3x)2+12xy+(2y)2

Check the middle term by multiplying 2ab2ab and compare this result with the middle term in the original expression.

2ab=2⋅(3x)⋅(2y)

Simplify.

2ab=12xy

Factor using the perfect square trinomial rule a²+2ab+b² = (a+b)² , where a=3x and b=2y.

(3x+2y)²

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2) We rewrite it as x² + 2x + 1 

We solve by using the formula (a+b)² = a2 + b2 + 2ab

We get, 

x² + (1)² + 2 (x) (1) 

= (x+1)² 

= (x+1) (x+1).

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3) 16x²+40xy+25y²

= (4x)2+2(4x)(5y)+(5y)²

= (4x+5y)²

= (4x+5y)(4x+5y)

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