Question

factorise the following using appropriate identities
1)9X^2+6xy+y^2
2)4y^2-4y+1
3)x^2-y^2/100

Answer 1

Hey Mate!

Here's ur answer dear:-)
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1) using identity (a+b)^2= a^2+2ab+b^2


$9x {}^{2} + 6xy + y {}^{2} \\ (3x) {}^{2} + 2 \times 3x \times y + (y) {}^{2} \\ (3x + y) {}^{2}$

2) using identity (a-b)^2= a^2-2ab+b^2


$4y {}^{2} - 4y + 1 \\ (2y) {}^{2} - 2 \times 2y \times 1 + 1 {}^{2} \\ (2y - 1) {}^{2}$

3)using identity a^2-b^2= (a+b)(a-b)


$x {}^{2} - \frac{y {}^{2} }{100 } \\ \\( x ){}^{2} - ( \frac{y}{10} ) {}^{2} \\ \\ (x + \frac{y}{10} )(x - \frac{y}{10} )$


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HOPE IT HELPS:-)

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Answer 2

$\bold{Answer :}$

1]

Now, 9x² + 6xy + y²

= (3x)² + (2 × 3x × y) + (y)²

= (3x + y)²,

using the identity : (a + b)² = a² + 2ab + b²

= (3x + y) (3x + y),

which is the required factorization.

2]

Now, 4y² - 4y + 1

= (2y)² - (2 × 2y × 1) + (1)²

= (2y - 1)²,

using the identity : (a - b)² = a² - 2ab + b²

= (2y - 1) (2y - 1),

which is the required factorization.

3]

Now, x² - (y²/100)

= (x)² - (y/10)²

= (x + y/10) (x - y/10),

using the identity : a² - b² = (a + b) (a - b)

which is the required factorization.

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