Question

4y²+9-12y-a²-b²+2ab
Please factorize the term with step by step explanation.

Answer 1

Answer:

(u³)² + (v³)² = u6 + v6. Can it be factored?

The answer is yes. As you may know, An+Bn can be factored on the reals if n is an odd integer:

An+Bn = (A+B) (An−1 − An−2B + An−3B2 ... − ABn−2 + Bn−1) for n odd

You’ve probably learned the simplest case, n = 3:

A³+B³ = (A+B) (A² − AB + B²)

So the solution is to rewrite u6+v6 as the sum of two cubes:

u6+v6 = (u²)³+(v²)³ = (u²+v²) ( (u²)² − u²v² + (v²)² ) = (u²+v²) (u4 − u²v² + v4)

Example 3: x10+1024y10 is a sum of squares, (x5)2 + (32y5)2. But it’s also a sum of fifth powers, (x2)5 + (4y2)5. Use the above factorization for the sum of fifth powers:

A5+B5 = (A+B) (A4 − A3B + A2B2 − AB3 + B4)

x10+1024y10 = (x2)5 + (4y2)5

=(x2+4y2) ( (x2)4 − (x2)3(4y2) + (x2)2(4y2)2 − (x2)(4y2)3 + (4y2)4 )

=(x2+4y2) (x8 − 4x6y2 + 16x4y4 − 64x2y6 + 256y8)

Answer 2

4y² = 4×y×y

9 = 3×3

-12y = -1×2×2×3×y

-a² = -1×a×a

-b = -1×b×b

2ab = 2×a×a

hope it will help u