Question

factorise plzzzzzzzzzzzzzzzzzzzzzz..

will follow u❤️​

Answer 1

Step-by-step explanation:

Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b).

\frac{{((p+q)(p-q))}^{3}+{({q}^{2}-{r}^{2})}^{3}+{({r}^{2}-{p}^{2})}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

((p+q)(p−q))

3

+(q

2

−r

2

)

3

+(r

2

−p

2

)

3

2 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b).

\frac{{((p+q)(p-q))}^{3}+{((q+r)(q-r))}^{3}+{({r}^{2}-{p}^{2})}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

((p+q)(p−q))

3

+((q+r)(q−r))

3

+(r

2

−p

2

)

3

3 Use Difference of Squares: {a}^{2}-{b}^{2}=(a+b)(a-b)a

2

−b

2

=(a+b)(a−b).

\frac{{((p+q)(p-q))}^{3}+{((q+r)(q-r))}^{3}+{((r+p)(r-p))}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

((p+q)(p−q))

3

+((q+r)(q−r))

3

+((r+p)(r−p))

3

4 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)

a

=x

a

y

a

.

\frac{{(p+q)}^{3}{(p-q)}^{3}+{((q+r)(q-r))}^{3}+{((r+p)(r-p))}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

(p+q)

3

(p−q)

3

+((q+r)(q−r))

3

+((r+p)(r−p))

3

5 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)

a

=x

a

y

a

.

\frac{{(p+q)}^{3}{(p-q)}^{3}+{(q+r)}^{3}{(q-r)}^{3}+{((r+p)(r-p))}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

(p+q)

3

(p−q)

3

+(q+r)

3

(q−r)

3

+((r+p)(r−p))

3

6 Use Multiplication Distributive Property: {(xy)}^{a}={x}^{a}{y}^{a}(xy)

a

=x

a

y

a

.

\frac{{(p+q)}^{3}{(p-q)}^{3}+{(q+r)}^{3}{(q-r)}^{3}+{(r+p)}^{3}{(r-p)}^{3}}{{(p-q)}^{3}+{(q-r)}^{3}+{(r-p)}^{3}}

(p−q)

3

+(q−r)

3

+(r−p)

3

(p+q)

3

(p−q)

3

+(q+r)

3

(q−r)

3

+(r+p)

3

(r−p)

3

hope it helps

Answer 2

Answer:

IN your question sum of

(p^{2} - q^{2} ) + (q^{2} - r^{2} ) + (r^{2} -p^{2} ) = 0(p2−q2)+(q2−r2)+(r2−p2)=0

Then their sum of cube will be equal to 3 times these no. such as (p^{2} - q^{2} )^3 + (q^{2} - r^{2} )^3 + (r^{2} -p^{2} ) ^3 = 3.(p^{2} - q^{2} ).(q^{2} - r^{2} ).(r^{2} -p^{2} )(p2−q2)3+(q2−r2)3+(r2−p2)3=3.(p2−q2).(q2−r2).(r2−p2)

similarly 

(p-q)^3 + (q-r)^3 + (r-p)^3 = 3.(p-q).(q-r).(r-p)(p−q)3+(q−r)3+(r−p)3=3.(p−q).(q−r).(r−p)

Thus

(p^{2} - q^{2} )^3 + (q^{2} - r^{2} )^3 + (r^{2} -p^{2} ) ^3 /(p-q)^3 + (q-r)^3 + (r-p)^3  

 =>  3.(p^{2} - q^{2} ).(q^{2} - r^{2} ).(r^{2} -p^{2} ) / 3.(p-q).(q-r).(r-p) 

=> (p-q)(p+q)(q-r)(q+r)(r-p)(r+p) / (p-q)(q-r)(r-p)  

=>  (p+q)(q+r)(r+p)