If a+b=10 and ab=16, find the value of a²– ab+b² and a²+ab+b².

Find the following products:

(i) (3x+2y)(9x²-6xy+4y²)

(ii) (4x-5y)(16x²+20xy+25y²)

(iii) (7p⁴+q)(49p⁸-7p⁴q+q²)

(iv)

(v)

(vi)

(vii)

(viii)

(ix) (1+x)(1+x+x²)

(x) (1+x)(1-x+x²)

(xi) (x²-1)(x⁴+x²+1)

(xii) (x³+1)(x⁶-x³+1)

If x = 3 and y = -1, find the values of each of the following using in identity:

(i) (9y² -4x²) (81y⁴ + 36x²y² +16x⁴)

(ii)

(iii)

(iv)

(v)

If a+b=8 and ab=6, find the value of a³+b³.

If a-b=6 and ab=20, find the value of a³-b³.