Question

factorise this 3:--

1.) x⁴ - 3x²y² + 9y⁴

2.) a²-2a - b² + 2b

3.) a⁴ + a²b² + b⁴​

Answer 1

Answer:

1.(x²+3xy+3y²)(x²-3xy+3y²)

2.(a-b) (a+b+2)

3.(a²+b²+ab)(a²+b² - ab)

Step-by-step explanation:

1.x⁴-3x²y²+9y⁴

= x⁴+9y⁴-3x²y²

= (x²)²+(3y²)²-3x²y²

= (x²+3y²)²-2.x².3y²-3x²y²

= (x²+3y²)²-6x²y²-3x²y²

= (x²+3y²)²-9x²y²

= (x²+3y²)²-(3xy)²

= (x²+3y²+3xy)(x²+3y²-3xy)

= (x²+3xy+3y²)(x²-3xy+3y²) Ans

2.If the a2 and b2 indicate the exponent, then divide the expression into two groups.

factor the first two terms as (a+ b) (a-b).

factor the last two terms as 2(a-b)

we have (a+b)(a-b) +2 (a-b)

note that a-b is a common factor to both groups.

then (a-b) (a+b+2)

3.a⁴+a²b²+b⁴

= (a² +b²)² - 2a²b² + a²b²

= (a²+b²)² - a²b²

= (a²+b²)² - (ab)²

now it is in the form of a² - b² =( a+ b)(a-b)

(a²+b²+ab)(a²+b² - ab)

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