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Expansion of (x^2 - y^2)

Write the fol...

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) ${(\frac{x}{y} + \frac{y}{z} + \frac{z}{x})}^{2}$

(ix) ${(\frac{a}{b c} + \frac{b}{c a} + \frac{c}{a b})}^{2}$

(x) $(x + 2 y + 4 z)^{2}$

(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 ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

Here

By applying in identity we get

${(- 3 x + y + z)}^{2} = {(- 3 x)}^{2} + y^{2} + z^{2} - 2 \times 3 x \times y + 2 y z - 2 \times (- 3 x) \times z$

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 ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

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 ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

Here

By applying in identity we get

Hence the expended form of is

(xi) Given

We shall use the identity ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

Here

By applying in identity we get

Hence the expended form of is

(xii) Given

We shall use the identity ${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

Here

By applying in identity we get

Hence the expended form of is.

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Similar questions

Write the following cubes in expanded form:

(i) $(2 x + 1)^{3}$

(ii) $(2 a - 3 b)^{3}$

(iii) $(\frac{3}{2} x + 1)^{3}$

(iv) $(x - \frac{2}{3} y)^{3}$

Expand each of the following, using suitable identities:

(i) (ii)

(iii) (iv)

(v) (vi)

Q. Question 6
Write the following cubes in expanded form:

(i) (2 x + 1)^{3} (i i) (2 a - 3 b)^{3} (i i i) {[\frac{3}{2} x + 1]}^{3} (i v) {[x - \frac{2}{3} y]}^{3}

Write the following cubes in expanded form:
(i) ${(2 x + 1)}^{3}$
(ii) ${(2 a - 3 b)}^{3}$

Write the following cubes in expanded form:
$(i) (2 x + 1)^{3}$
$(i i) (2 a - 3 b)^{3}$
$(i i i) {[\frac{3}{2} x + 1]}^{3}$
$(i v) {[x - \frac{2}{3} y]}^{3}$

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