Question

expand :

1.(a+b-c)^2
2.(a-2b-5c)^2
3.(3a-2b-5c)^2

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Answer 1

1.(a+b-c)^2

Can be expressed as

=(a+b-c)*(a+b-c)

On expansion of the above expression

=a*(a+b-c)+b*(a+b-c)-c*(a+b-c)

=a^2+ab-ac+ba+b^2-bc-ca-cb+c^2

Rearrange the above equation

=a^2+b^2+c^2+ab+ba-ac-ca-bc-cb

Rearrange by commutative property

=a^2+b^2+c^2+ab+ab-ac-ac-bc-bc

=a^2+b^2+c^2+2ab-2ac-2bc

On taking out the common terms, the expansion results in the final answer

=a^2+b^2+c^2+2(ab-ac-bc)

2.(a+b+c)^2 = a^2+b^2+c^2+2ab+2bc+2ac

=(a+2b+5c)^2 = a^2+4b^2+25c^2+40ab+20bc+10ac

3.We have (x+y+z)^2

=x^2 +y^2 +z^2 +2(xy+yz+zx)

Take x=3a,y=−2b and z=5c

(3a−2b+5c)^2

=(3a)^2 +(−2b)^2 +(5c)^2 +2(3a×−2b+(−2b)×5c+5c×3a)

=9a^2 +4b^2 +25c^2 +2(−6ab−10bc+15ac)

=9a^2 +4b^2 +25c^2 −12ab−20bc+30ac

∴(3a−2b+5c)^2 = 9a^2 +4b^2 +25c^2 −12ab−20bc+30ac