Factorize :
${(2 a - 3)}^{2} - 2 (2 a - 3) (a - 1) + {(a - 1)}^{2}$

{(a + 2)}^{2}

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{(a - 2)}^{2}

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{(a - 3)}^{2}

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{(a + 3)}^{2}

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Solution

The correct option is C ${(a - 2)}^{2}$
${(2 a - 3)}^{2} - 2 (2 a - 3) (a - 1) + {(a - 1)}^{2}$
Using,
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$= (2 a - 3 - a + 1)^{2}$
$= (a - 2)^{2}$

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Factorize : (2a−3)2−2(2a−3)(a−1)+(a−1)2

The correct option is C (a−2)2(2a−3)2−2(2a−3)(a−1)+(a−1)2Using,(a−b)2=a2−2ab+b2=(2a−3−a+1)2=(a−2)2

Factorize :
${(2 a - 3)}^{2} - 2 (2 a - 3) (a - 1) + {(a - 1)}^{2}$

The correct option is C ${(a - 2)}^{2}$
${(2 a - 3)}^{2} - 2 (2 a - 3) (a - 1) + {(a - 1)}^{2}$
Using,
$(a - b)^{2} = a^{2} - 2 a b + b^{2}$
$= (2 a - 3 - a + 1)^{2}$
$= (a - 2)^{2}$