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Bruce
Mathematics
15 September, 01:02
What is the completely factored form of d4-8d2+16
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Aydan Johnson
15 September, 01:21
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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!
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