Question

Which statement about (a2 − 4)(a4 + 4a2 + 16) is correct?

Answer 1

Answer:

the expression is equivalent and is completely factored. the expression is equivalent, but the (a2 – 4) term is not completely factored.

Answer 2

Given:

Which statement about (a2 − 4)(a4 + 4a2 + 16) is correct?

Solution:

Simplify $\[\left( {{a^2} - 4} \right)\left( {{a^4} + 4{a^2} + 16} \right)\]$

Know that,

$\[\begin{array}{l}\left( {{a^2} - {b^2}} \right) = \left( {a + b} \right)\left( {a - b} \right)\\{\left( {a + b} \right)^2} = {a^2} + {b^2} + 2ab\end{array}\]$

Therefore,

$\[\begin{array}{l} = \left( {{a^2} - 4} \right)\left( {{a^4} + 4{a^2} + 16} \right)\\ = \left( {{a^2} - {2^2}} \right)\left\{ {{{\left( {{a^2}} \right)}^2} + 2 \times 2{a^2} + {4^2}} \right\}\\ = \left( {{a^2} - {2^2}} \right){\left( {{a^2} + {2^2}} \right)^2}\\ = \left( {{a^2} - {2^2}} \right)\left( {{a^2} + {2^2}} \right)\left( {{a^2} + {2^2}} \right)\\ = \left( {{a^4} - {2^4}} \right)\left( {{a^2} + {2^2}} \right)\end{array}\]$

Hence, the required answer is $\[\left( {{a^4} - {2^4}} \right)\left( {{a^2} + {2^2}} \right)\]$.