Question

factorise
8(x+y)³-50(x+y)​

Answer 1

Answer:

2 • (x + y) • (4x2 + 8xy + 4y2

Step-by-step explanation:

(8 • ((x + y)3)) - 50 • (x + y)

STEP

2 :- Equation at the end of step 2

8 • (x + y)3 - 50 • (x + y)

STEP

3 :- Pulling out like terms

3.1

Pull out x+y

After pulling out, we are left with :

(x+y) • ( 8 * (x+y)2 +( 50 * (-1) )) 3.2 Evaluate : (x+y)2 = x2+2xy+y2

STEP

4

:

Pulling out like terms

4.1 Pull out like factors :

8x2 + 16xy + 8y2 - 50 =

2 • (4x2 + 8xy + 4y2 - 25)

Final result :

2 • (x + y) • (4x2 + 8xy + 4y2

Answer 2

Step-by-step explanation:

$$\begin{lgathered}= 2(x+y) [ 4(x+y)^{2} - 25 ]\\= 2(x+y) [ 2^{2}(x+y)^{2} - 5^{2} ] \\= 2(x+y) [ (2x+2y)^{2} - 5^{2}]\\=2(x+y)[ (2x+2y+5)(2x+2y-5)]\end{lgathered}$$

$$\boxed { \pink { Since, \:a^{2} - b^{2} = ( a + b )( a - b )}}$$

$$= 2(x+y)(2x+2y+5)(2x+2y-5)$$

Therefore.,

$$\red {Factorisation \:of \: 8(x+y)^{3} - 50(x+y) }$$

$$\green { = 2(x+y)(2x+2y+5)(2x+2y-5)}$$