f.2maths.....very easy!15marks!!

1. Factorize the polynomials by using identities.
(a) 8x^3-1=(2x)^3-1=(2x-1)(4x^2+2x+1)
(b) 27+z^3=3^3+z^3=(z+3)(z^2-3z+9)

2. Factorize the polynomials by cross method.
(a) x^2-14x-72=(x-18)(x+4)
(b) 4x^2-4x-15=(2x+3)(2x-5)
(c) 3x^2-7x-6=(x-3)(3x+2)
(d) 2x^2-22x+48=2(x-3)(x-8)
(e) 6x^3-48y^3=6(x^3-(2y)^3)=6(x-2y)(x^2+2xy+4y^2)
(f) 54y^3+2x^3z^6=2((xz^2)^3+(3y)^3)
=2(xz^2+3y)(x^2z^4-3xyz^2+9y^2)
(g) 2x^2+5x-12=(2x-3)(x+4)

3.(a) Factorize x^4-6x^2+9=(x^2-3)^2
(b) Hence, factorize x^4-6x^2+9-4x^2
=(x^2-3)^2-(2x)^2
=(x^2-3-2x)(x^2-3+2x)
=(x+1)(x-3)(x-1)(x+3)

4. Correct the mistake in each of the following questions.
(a) x^4-1=(x^2)^2-1
=(x^2+1)(x^2-1)=(x^2+1)(x-1)(x+1)
(b) x^3-27y^3=(x-3y)^3
x^3-27y^3=x^3-(3y)^3
=(x-3y)(x^2+3xy+9y^2)