Question

simplify using formula
$(4 {a}^{2} - 9)( 4{a}^{2} - 6a + 9)(4a ^{2} + 6a + 9)$
​

Answer 1

Answer:

(2a-3)(2a+3)(4a^2-6a+9)(4a^2+6a+9)

Step-by-step explanation:

factorize 4a^2-9

we get

(2a-3)(2a+3)

so final answer is,

(2a-3)(2a+3)(4a^2-6a+9)(4a^2+6a+9)

(we cant factorize other 2 terms)

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Answer 2

$\displaystyle\huge\red{\underline{\underline{Solution}}}$

FORMULA TO BE IMPLEMENTED

We are aware of the below mentioned Identity :

1.

${a}^{2} - {b}^{2} = (a + b)(a - b)$

2.

${a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

3.

${a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$

TO EVALUATE

$(4 {a}^{2} - 9)(4 {a}^{2} + 6a + 9)(4 {a}^{2} - 6a + 9)$

EVALUATION

$(4 {a}^{2} - 9)(4 {a}^{2} + 6a + 9)(4 {a}^{2} - 6a + 9)$

$= \{ {(2a)}^{2} - {(3)}^{2} \}(4 {a}^{2} + 6a + 9)(4 {a}^{2} - 6a + 9)$

$= (2a + 3)(2a - 3)(4 {a}^{2} + 6a + 9)(4 {a}^{2} - 6a + 9)$

$= (2a + 3) \{{(2a)}^{2} - 2a \times 3 + {(3)}^{2} \} (2a - 3) \{{(2a)}^{2} + 2a \times 3 + {(3)}^{2} \}$

$= \{{(2a)}^{3} + {(3)}^{3} \} \times \: \{{(2a)}^{3} - {(3)}^{3} \}$

$= (8 {a}^{3} + 27) \times (8 {a}^{3} - 27)$

$= {(8 {a}^{3}) }^{2} - {(27)}^{2}$

$= 64 {a}^{6} - 729$