Question

simplify (a - 2b )(a + 2b)(a² + 4b²)(a⁴ + 16b⁴)

Answer 1

hey, here is your answer

$(a - 2b)(a + 2b)( {a}^{2} + {4b}^{2} )( {a}^{4} + {16b}^{4} ) \\ \\ ( {a}^{2} - ( {2b})^{2})( {a}^{2} + {4b}^{2} )( {a}^{4} + {16a}^{4} ) \\ ( {a}^{2} - {4b}^{2} )( {a}^{2} + {4b}^{2} )( {a}^{4} + {16b}^{4} ) \\ \\ ( { {a}^{2} )}^{2} - { {(4b}^{2} )}^{2} ( {a}^{4} + {16b}^{4} ) \\ ( {a}^{4} - {16b}^{4} )( {a}^{4} + {16b}^{4} ) \\ \\ { ({a}^{4} )}^{2} - { ({16b}^{4} )}^{2} \\ \\ {a}^{8} - 256 {b}^{8}$
hope this helps you
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Answer 2

HEY HERE IS YOUR ANSWER ☺☺☺

We can easily find the resulting product by using identity (a + b) (a - b) = a^2 - b^2

But remember we will solve it step by step from the first one to last one .

First one (a - 2b) (a + 2b)
Identity used = (a + b) (a - b) = a^2 - b^2
where a = a and b = 2b.

$(a - 2b)(a + 2b) = {(a)}^{2} - {(2b)}^{2} = {a}^{2} - {4b}^{2}$

Second binomial = (a^2 +4b^2)
Result from first product = (a^2 - 4b^2)

We can easily find their product by using the first identity (a + b) (a - b) = a^2 - b^2.
Where a = a^2 and b = 4b^2.

$( {a}^{2} + {4b}^{2} )( {a}^{2} - {4b}^{2} ) = { ({a}^{2} )}^{2} - { {(4b}^{2} )}^{2} = ( {a}^{4} - {16b}^{4} )$

Third binomial =( a^4 + 16b^4)
Result from second product = (a^4 - 16b^4)

We can easily find the resulting product by using identity (a + b) ( a - b) = a^2 - b^2
where a = a^4 and b = 16b^4

$( {a}^{4} + {16b}^{4} )( {a}^{4} - {16b}^{4} ) = {( {a}^{4}) }^{2} - ({ {16b}^{4} })^{2} = ({a}^{8} - {256b}^{8} )$

So the resulting product is:- a^8 - 256b^8

HOPE MY ANSWER HELPED☺☺☺
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