Question

1. expand each of the following.

(a) $(x^2 + 1)(x + 2)$
(b) $(2 + y)(1 - y^2)$

Explanation:

Step1: Apply distributive property (a)

$(x^2+1)(x+2) = x^2(x+2) + 1(x+2)$

Step2: Expand each term (a)

$= x^3 + 2x^2 + x + 2$

Step3: Apply distributive property (b)

$(2+y)(1-y^2) = 2(1-y^2) + y(1-y^2)$

Step4: Expand each term (b)

$= 2 - 2y^2 + y - y^3$

Answer:

(a) $x^3 + 2x^2 + x + 2$
(b) $2 - 2y^2 + y - y^3$