Question

Evaluate (a+bc)(a-bc)(a^2+(b^2)(c^2))

Answer 1

$(a+bc)(a-bc)[ a^{2} + (b^{2} )(c^{2})]$

/* By algebraic identity */

$\boxed{ \pink{ x^{2} - y^{2} = (x+y)(x-y) }}$

$= [ a^{2} - (bc)^{2}] [ a^{2} + (bc)^{2}]$

$= ( a^{2} )^{2} - [(bc)^{2}]^{2}$

$= a^{4} - (bc)^{4}$

$= a^{4} - b^{4}c^{4}$

Therefore.,

$\red{(a+bc)(a-bc)[ a^{2} + (b^{2} )(c^{2})]}$

$\green {= a^{4} - b^{4}c^{4} }$

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Answer 2

Answer:

$(a+bc)(a-bc)[ a^{2} + (b^{2} )(c^{2})]$

/* By algebraic identity */

$\boxed{ \pink{ x^{2} - y^{2} = (x+y)(x-y) }}$

$= [ a^{2} - (bc)^{2}] [ a^{2} + (bc)^{2}]$

$= ( a^{2} )^{2} - [(bc)^{2}]^{2}$

$= a^{4} - (bc)^{4}$

$= a^{4} - b^{4}c^{4}$

Therefore.,

$\red{(a+bc)(a-bc)[ a^{2} + (b^{2} )(c^{2})]}$

$\green {= a^{4} - b^{4}c^{4} }$