Question

1) If bc=b-c and c=-1, find the value of bc

2)Factorise x^2+(a-b)x-ab

3) If x= 1/2y, express (x-y)(x^2-y^2)(x^3-y^3) in terms of y.

Answer 1

1)

$$b(-1)=b-(-1)=>2b=-1=>b=-\dfrac{1}{2}$$

$$bc=-\dfrac{1}{2}(-1)=\dfrac{1}{2}$$

2)

$$x^2+(a-b)x-ab=(x^2-bx)+(ax-ab)$$

$$=x(x-b)+a(x-b)=(x+a)(x-b)$$

3)

$$(x-y)(x^2-y^2)(x^3-y^3)$$

$$=(\dfrac{1}{2}y-y)(\dfrac{1}{4}y^2-y^2)(\dfrac{1}{8}y^3-y^3)$$

$$=-\dfrac{21}{64}y^6$$