Factorise the following using appropriate identities- -1 MARK- 4y2 - 4y - 1

Formula: 0.5 Mark Application: 0.5 Mark 4y^2 – 4y + 1 = (2y)^2 nbsp;– 2(2y)(1) + 1^2 comparing with above identity(a b)^2 nbsp; = a^2 – 2ab nbsp;+ b^2 ...

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Standard IX

Mathematics

Algebraic Identities

Factorise the...

Question

Factorise the following using appropriate identities:
$4 y^{2} - 4 y + 1$

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Solution

Given $4 y^{2} - 4 y + 1$

$= {(2 y)}^{2} - 2 (2 y) (1) + 1^{2}$

As we know that ${a^{2} - 2 a b + b^{2} = (a - b)}^{2}$
Substitute $a = 2 y$ anf $b = 1$ in above formula, we get
$\Rightarrow (2 y)^{2} - 2 (2 y) (1) + (1)^{2} = (2 y - 1)^{2}$
Therefore, the factors of the given expression are $= {(2 y - 1)}^{2}$

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Factorise the following using appropriate identities: 4y2–4y+1

Given 4y2–4y+1 =(2y)2–2(2y)(1)+12 As we know that a2–2ab+b2=(a−b)2Substitute a=2y anf b=1 in above formula, we get ⇒(2y)2−2(2y)(1)+(1)2=(2y−1)2Therefore, the factors of the given expression are =(2y−1)2

Factorise the following using appropriate identities:
$4 y^{2} - 4 y + 1$