1

${(a + b)}^{2} = a^{2} + a b + b a + b^{2} = a^{2} + 2 a b + b^{2}$
${(a - b)}^{2} = (a - b) (a - b) = a^{2} - a b - b a + b^{2} = a^{2} - 2 a b + b^{2}$
$(a + b) (a - b) = a^{2} - a b + b a - b^{2} = a^{2} - b^{2}$

2

${(a + b)}^{2} = (a + b) \cdot (a + b)$ is de oppervlakte van het hele vierkant.
$a^{2}$ , $a b$ , $a b$ en $b^{2}$ zijn de oppervlaktes van de vier stukken.

3

a

$3 x^{2} + 6 x + 3$
$9 x^{2} - 6 x + 1$
$9 x^{2} - 1$

b

$x^{2} + 2 x + 1 - (x^{2} - 2 x + 1) = 4 x$
$x^{2} + 2 x + 1 + (x^{2} - 2 x + 1) = 2 x^{2} + 2$
${(x^{2} - 1)}^{2} = {(x^{2})}^{2} - 2 x^{2} + 1 = x^{4} - 2 x^{2} + 1$

4

a

$a^{2} - (a^{2} - b^{2}) = a^{2} - a^{2} + b^{2} = b^{2}$

b

Je neemt voor $a$ steeds $n$ en voor $b$ achtereenvolgens 1, 2 en 3.

5

${(x + 8)}^{2}$	${(x - 8)}^{2}$	$(x - 8) (x + 8)$
${(x - 3)}^{2}$	$(x - 10) (x + 10)$	${(x - 6)}^{2}$
${(2 x + 3)}^{2}$	${(2 x - 3)}^{2}$	$(2 x - 3) (2 x + 3)$
${(10 x + y)}^{2}$	${(10 x - y)}^{2}$	$(10 x - y) (10 x + y)$