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Question

Write the following in the expanded form:

(i) (a +2b + c)2

(ii) (2a − 3b − c)2

(iii) (−3x + y + z)2

(iv) (m + 2n − 5p)2

(v) (2 + x − 2y)2

(vi) (a2 + b2 + c2)2

(vii) (ab + bc + ca)2

(viii) xy+yz+zx2

(ix) abc+bca+cab2

(x) (x+2y+4z)2

(xi) (2x − y + z)2

(xii) (−2x + 3y + 2z)2

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Solution

In the given problem, we have to find expended form

(i) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(ii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(iii) Given

We shall use the identity a+b+c2=a2+b2+c2+2ab+2bc+2ca

Here

By applying in identity we get

-3x+y+z2=-3x2+y2+z2-2×3x×y+2yz-2×-3x×z

Hence the expended form of
is.

(iv) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(v) Given

We shall use the identity a+b+c2=a2+b2+c2+2ab+2bc+2ca

Here

By applying in identity we get

Hence the expended form of is.

(vi) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is.

(vii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form ofis .

(viii) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(ix) Given

We shall use the identity

Here

By applying in identity we get

Hence the expended form of is

(x) Given

We shall use the identity a+b+c2=a2+b2+c2+2ab+2bc+2ca

Here

By applying in identity we get

Hence the expended form of is

(xi) Given

We shall use the identity a+b+c2=a2+b2+c2+2ab+2bc+2ca

Here

By applying in identity we get

Hence the expended form of is

(xii) Given

We shall use the identity a+b+c2=a2+b2+c2+2ab+2bc+2ca

Here

By applying in identity we get

Hence the expended form of is.


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