Express as a polynomial. (a+b+c+d)^{2}

William Collins

William Collins

Answered question

2021-12-10

Express as a polynomial.
(a+b+c+d)2

Answer & Explanation

maul124uk

maul124uk

Beginner2021-12-11Added 35 answers

Step 1
Use the identity (x+y)2=x2+y2+2xy.
Step 2
Replace x with a+b+c and y with d in the identity (x+y)2=x2+y2+2xy.
[(a+b+c)+d]2=(a+b+c)2+2(a+b+c)d+d2
Step 3
Use the property (x+y+z)2=x2+y2+z2+2xy+2yz+2xz.
[(a+b+c)+d]2=(a+b+c)2+2(a+b+c)d+d2
=a2+b2+c2+2ab+2bc+2ac+2ad+2bd+2cd+d2
Step 4
Conclusion:
a2+b2+c2+2ab+2bc+2ac+2ad+2bd+2cd+d2

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