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Expansion of (x+a)(x+b)

Simplify each...

Question

Simplify each of the following products:

(i) $(\frac{1}{2} a - 3 b) (3 b + \frac{1}{2} a) (\frac{1}{4} a^{2} + 9 b^{2})$

(ii) ${(m + \frac{n}{7})}^{3} (m - \frac{n}{7})$

(iii) $(\frac{x}{2} - \frac{2}{5}) (\frac{2}{5} - \frac{x}{2}) - x^{2} + 2 x$

(iv) $(x^{2} + x - 2) (x^{2} - x + 2)$

(v) $(x^{3} - 3 x^{2} - x) (x^{2} - 3 x + 1)$

(vi) $(2 x^{4} - 4 x^{2} + 1) (2 x^{4} - 4 x^{2} - 1)$

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Solution

(i) In the given problem, we have to find product of

We have been given

On rearranging we get,

We shall use the identity

By substituting,we get,

We shall use the identity

Hence the value of is

(ii) In the given problem, we have to find product of

We have been given

On rearranging we get

We shall use the identity

By substituting,, we get ,

Hence the value of is

(iii) In the given problem, we have to find product of

On rearranging we get

We shall use the identity

By substituting ,

Hence the value of is

(iv) In the given problem, we have to find product of

On rearranging we get

We shall use the identity

Hence the value of is

( v) In the given problem, we have to find product of

Taking as common factor

We shall use the identity

Hence the value of is

(vi) In the given problem, we have to find product of

On rearranging we get

We shall use the identity

Hence the value of is.

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Similar questions

Q. Simplify each of the following products:

(i)

(\frac{1}{2} a - 3 b) (3 b + \frac{1}{2} a) (\frac{1}{4} a^{2} + 9 b^{2})

{(m + \frac{n}{7})}^{3} (m - \frac{n}{7})

Q. Simplify each of the following products:
(i)

(\frac{x}{2} - \frac{2}{5}) (\frac{2}{5} - \frac{x}{2}) - x^{2} + 2 x

(x^{2} + x - 2) (x^{2} - x + 2)

(x^{3} - 3 x^{2} - x) (x^{2} - 3 x + 1)

(2 x^{4} - 4 x^{2} + 1) (2 x^{4} - 4 x^{2} - 1)

Q. Find the limits :

i .

lim x \to 1 [\frac{x^{2} + 1}{x + 100}]

i i .

lim x \to 2 [\frac{x^{3} - 4 x^{2} + 4 x}{x^{2} - 4}]

i i i .

lim x \to 2 [\frac{x^{2} - 4}{x^{3} - 4 x^{2} + 4 x}]

i v .

lim x \to 2 [\frac{x^{3} - 2 x^{2}}{x^{2} - 5 x + 6}]

v .

lim x \to 1 [\frac{x - 2}{x^{2} - x} - \frac{1}{x^{3} - 3 x^{2} + 2 x}]

\int \frac{2 x^{4} + x^{3} - 4 x^{2} + 4 x + 2}{(x^{2} + 4) (x^{2} - 1)^{2}} d x

Simplify the expressions below

(i)

(ii)

(iii)

(iv)

(v)

(vi)

(vii)

(viii)

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