Question

23. Factorise: 6 - 24(x-y)^2​

Answer 1

Step-by-step explanation:

Simplify

1

Expand the square

6−24(−)2

6−24(−)(−)

2

Distribute

6−24(−)(−)

6−24((−)−(−))

3

Distribute

6−24((−)−(−))

6−24(2−−(−))

4

Distribute

6−24(2−−(−))

6−24(2−−+2)

5

Combine like terms

6−24(2−−+2)

6−24(2−2+2)

6

Distribute

6−24(2−2+2)

6−242+48−242

7

Rearrange terms

6−242+48−242

−242+48−242+6

Answer 2

To Factorise :

6 - 24(x - y)²

Solution :

→ 6 - 24(x - y)²

→ 6 - 24(x - y)(x - y)

→ 6 - 24(x(x - y) - y(x - y))

→ 6 - 24(x² - xy)(xy + y²)

→ 6 - 24(x² - 2xy + y²)

→ 24x² - 48xy + 24y² + 6

∴ Required answer :

Answer is :

• 24x² - 48xy + 24y² + 6

Verification :

24x² - 48xy + 24y² + 6

→ 6 - 24(x² - xy)(xy + y²)

→ 6 - 24(x(x - y) - y(x - y))

→ 6 - 24(x - y)(x - y)

→ 6 - 24(x - y)²

• Hence, Verified!