Evaluate the following by using identities:
(i) 98³
(ii) 1001³

Simplify: \(\left[ \frac { ({ x }^{ 2 }-{ y }^{ 2 })^{ 3 }+({ y }^{ 2 }-{ z }^{ 2 })^{ 3 }+({ z }^{ 2 }-{ x }^{ 2 })^{ 3 } }{ (x-y)^{ 3 }+(y-z)^{ 3 }+(z-x)^{ 3 } } \right] \) by using identity

If a = 4, b = 5 and c = 6 , then find the value of \(\left[ \frac { (ab+bc+ca-{ a }^{ 2 }-{ b }^{ 2 }-{ c }^{ 2 }) }{ (3abc-{ a }^{ 3 }-{ b }^{ 3 }-{ c }^{ 3 }) } \right] \).

Factorise 2x²-15x+27

Factorise 2x² + 15x - 27

Factorise (x + y)² + 9(x +  y) + 20

Factorise the following:
(i) 2a²+9a+10
(ii) 5x²- 29xy - 42y²
(iii) 9 -18x + 8x²
(iv) 6x²+16xy + 8y²
(v) 12x²+ 36x²y + 27y²x²
(vi) (a + b)² + (a + b) +18

Find the quotient and remainder for the following using synthetic division:
(i) (x³+x²-7x-3) ÷ (x - 3)
(ii) (x³+2x²-x-4) ÷ (x + 2)
(ii) (3x³-2x²+7x-5) ÷ (x + 3)
(iv) (8x⁴-2x²+6x+5) ÷ (4x + 1)

Factorise x³− 5x²−2x + 24

Factorise each of the following polynomials using synthetic division:
(i) x³-3x²-10x +24
(ii) 2x³-3x²-3x+2
(iii) −7x+3+ 4x³
(iv) x³+x²-14x-24
(v) x³-7x+6
(vi) x³-10x²-x+10