Question

solve=x⁴ -(y+z)²
use identity = a²-b²​

Answer 1

Answer:

Using the identity a

2

−b

2

=(a+b)(a−b)

Using the above identity, the expression x

4

−625 can be factorised as follows:

x

4

−625=(x

2

)

2

−(25)

2

=(x

2

−25)(x

2

+25)=(x−5)(x+5)(x

2

+25)

Hence, x

4

−625=(x−5)(x+5)(x

2

+25)

Answer 2

x⁴ -(y+z)² =(x² + y + z) (x² -  y - z)

Given:

• x⁴ -(y+z)²

To Find:

• Factors

Solution:

Factorization is finding factors which when multiplied together results in the original number.

x⁴ -(y+z)²

Step 1:

Rewrite x⁴ as (x²)²   using law of exponent

= (x²)²  - (y+z)²

Step 2:

use identity   a²-b²​ = (a + b)(a - b)

where a = x² and b = (y + z)

=(x² + y + z) (x² - (y + z)

=(x² + y + z) (x² -  y - z)

Hence x⁴ -(y+z)² =(x² + y + z) (x² -  y - z)