What is the completely factored form of d4-8d2+16

Solution:

1) Rewrite it in the form {a}^{2}-2ab+{b}^{2}, where a={d}^{2} and b=4

{ ({d}^{2}) }^{2}-2 ({d}^{2}) (4) + {4}^{2}

2) Use Square of Difference: { (a-b) }^{2}={a}^{2}-2ab+{b}^{2}

{ ({d}^{2}-4) }^{2}

3) Rewrite {d}^{2}-4 in the form {a}^{2}-{b}^{2} , where a=d and b=2

{ ({d}^{2}-{2}^{2}) }^{2}



4) Use Difference of Squares: {a}^{2}-{b}^{2} = (a+b) (a-b)

{ ((d+2) (d-2)) }^{2}

5) Use Multiplication Distributive Property: { (xy) }^{a}={x}^{a}{y}^{a}

{ (d+2) }^{2}{ (d-2) }^{2}

Done!