IB Maths AA SL AA 1.3 practice question

Paper 2, calculatorMedium7 marks

Let $A(x)=(x+1)^2-1$ and $B(x)=x(x+2)$ where $x\in\mathbb{R}$

(a)

Find $A(3)$ and $B(3)$

[2]

(b)

Starting with $A(x)$ show by a chain of algebraic equalities that $A(x)$ has the same value as $B(x)$ for every $x\in\mathbb{R}$

[3]

(c)

Complete each statement using either $=$ or $\equiv$

A(3)\ \square\ B(3)

A(x)\ \square\ B(x),\quad \text{for all }x\in\mathbb{R}

[2]