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Chapter 7. The Pythagorean theorem

Note. The hypotenuse is the longest side of the triangle: $BC > AB$, $BC > AC$.

Example. With AB = 3 cm and AC = 4 cm:

Worksheet. Linear equations

Exercise 1. Solve the following equations.

a) $3x - 7 = 2x + 5$

b) $\dfrac{x}{4} + 1 = \dfrac{2x - 3}{3}$

Exercise 2. Expand and simplify.

a) $A = (2x + 3)(x - 5)$

b) $B = (3x - 1)^2 - (x + 2)^2$

Exercise 3. Compute and give the result as a fraction in lowest terms.

Test 4. Algebraic expressions

Exercise 1 3 pts

Factor the following expressions.

a) $x^2 - 9$

b) $4x^2 + 12x + 9$

Exercise 2 2 pts

Solve the equation.

Answer key. Test 4

Exercise 1

a) $x^2 - 9 = (x - 3)(x + 3)$

b) $4x^2 + 12x + 9 = (2x + 3)^2$

Exercise 2

The solutions are $-3$ ; $\dfrac{1}{2}$.

Well justified 5/5