Factorisation Test - 8

zero means root x + 2 = 0   ⇒ x = −2.

(x + y)(x − y) x² − y² = A binomial.

 (x² − x)² By physical inspection and mental calculation, we can see that highest term will be =x⁴ = 4 ⇒ degree = 4, ALITER, by actual calculation (x² − x)² = [x(x − 1)]² 

=x²(x − 1)² x²(x² − 2x + 1)             x⁴ − 2x³ + x² So we get, →x⁴ as highest term ⇒ Degree = 4.

 Just put the value of 'a' & 'b' Or Write a² + b² + 2ab = (a + b)² Now put a = 2, b = 1 = (2 + 1)² = 9.  

Multiply (x + a)(x − b) term by term =(x + a)x + (x + a)(−b) = x² + ax − bx − ab = x² + (a − b)x − ab.

Inspection shows that 9x²y² is common factor: 9x²y² {2xy − 3y + 4x} Further factors are not possible.

mn(u² − v²) − uv(m² + n²) = u²mn + v²mn = − uvm² − uvn² = un(um − vn) + vm(vn − um)  = un(um − vn) − vm(um − un) = (un −  vm)(um − vn).

Taking (p+q) factors as common,(p + q){2p + 5 − (p + 3)}  = (P + q{p + 2}.

(x − y)(x + y)(x² + y²){(x² + y²) − 2x²y²} Combining from left in bunches of two factors each, (x − y)(x + y) = x² − y² Then (x² − y²)(x² + y²) = x⁴ − y⁴ Then, (x⁴ − y⁴)(x⁴ + y⁴) =

x⁸ − y⁸ [since{(x² + y²)² − 2x²y²} = x⁴ + y⁴].