Question

please solve this question of factorization​

Answer 1

Question:

Factorize:

a³ - 144 a

Answer:

➙ a ( a + 12 ) ( a - 12 )

Step - by step Explanation:

➙ a³ - 144 a

Taking out the common factors:

• When each term of a given expression contains a common factor, divide each term by this factor and enclose the quotient within the brackets, keeping the common factor outside the bracket.

As in the expression above 'a' is the common factor in both the times so keeping the common factor 'a' outside the bracket and then keeping the common factor outside the bracket 'a'.

➙ a ( a² - 144 )

Now, we know that 12 × 12 = 144 i.e., 12² = 144

So,

➙ a ( a² - 12² )

Difference of two square:

• Since the product of ( x + y ) and ( x - y )
• ( x + y ) ( x - y ) = x² - y²

∴ Factors of x² - y² are ( x + y ) ( x - y )

• i.e, x² - y² = ( x + y ) ( x - y )

➙ a ( a + 12 ) ( a - 12 )

Some more such questions:

➩ x² - 25

➩ x² - 5²

➩ ( x + 5 ) ( x - 5 )

➩ 48x³ - 27x

➩ 3x ( 16x² - 9 )

➩ 3x [ ( 4x )² - ( 3 )² ]

➩ 3x ( 4x + 3 ) ( 4x - 3 )

➩ 32x³ - 8x

➩ 2x ( 16x² - 4 )

➩ 2x [ ( 4x )² - ( 2 )² ]

➩ 2x ( 4x + 2 ) ( 4x - 2 )

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Answer 2

$\begin{gathered}\Large{\bold{\purple{\underline{Formula \: Used \::}}}} \end{gathered}$

$1. \: \boxed{ \red {\tt \: {x}^{2} - {y}^{2} = (x + y)(x - y)}}$

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$\large\underline\purple{\bold{Solution :- }}$

$:  \implies \bf \: {a}^{3} - 144a$

$:  \implies \tt \: a ( {a}^{2} - 144)$

$:  \implies \tt \: a( {a}^{2} - {(12)}^{2} )$

$:  \implies \tt \: a(a - 12)(a + 12)$

$:  \implies \boxed{ \red{ \tt \: { {a}^{3} - 144a} = \tt \: a(a - 12)(a + 12)}}$

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Additional Information :-

$1. \: \boxed{ \red {\tt \: {(x + y)}^{2} = {x}^{2} + {y}^{2} + 2xy}}$

$2. \: \boxed{ \blue {\tt \: {(x - y)}^{2} = {x}^{2} + {y}^{2} - 2xy}}$

$3. \: \boxed{ \red {\tt \: {(x + y)}^{2} - {(x - y)}^{2} = 4xy}}$

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