Question

Factorise:
(a + 3)2 - 8 (a + 3) + 16​

Answer 1

SOLUTION

TO FACTORISE

$\sf{ {(a + 3)}^{2} - 8(a + 3) + 16 }$

FORMULA TO BE IMPLEMENTED

We are aware of the identity that

$1. \: \: \: \sf{ {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2} }$

$2. \: \: \: \sf{ {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }$

EVALUATION

$\sf{ {(a + 3)}^{2} - 8(a + 3) + 16 }$

$= \sf{ {a}^{2} +2.a .3+ 9 - 8a - 24+ 16 } \: (by \: formula \: 1)$

$= \sf{ {a}^{2} + 6a + 9 - 8a - 24+ 16 }$

$= \sf{ {a}^{2} - 2a + 1 }$

$= \sf{ {a}^{2} - 2.a.1 + {(1)}^{2} }$

$= \sf{ {(a - 1)}^{2} } \: \: \: \: (by \: formula \: 2)$

$= \sf{(a - 1)(a - 1)}$

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Answer 2

Given : (a + 3)² - 8 (a + 3) + 16​

To Find :  Factorize

Solution:

(a + 3)² - 8 (a + 3) + 16​

= (a + 3)² - 2(4) (a + 3) + 4²

Use (x  - y)²  = x²  - 2xy + y²

x  = a  + 3

y = 4

= (a + 3 - 4)²

= (a - 1)²

= (a - 1)(a - 1)

(a + 3)² - 8 (a + 3) + 16​   =   (a - 1)(a - 1)

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