Working with formulas

Working with formulas > Rewriting formulas

Overview

1234Rewriting formulas

Exercises

Exercise 1

Rewrite these formulas into their simplest form:

$4 \cdot x + 10 = 3 \cdot x - 2 \cdot y$

$2 \cdot y + 2 \cdot x \cdot x + 4 \cdot x = 6 \cdot x^{2}$

$4 \cdot x \cdot h + 2 \cdot x^{2} = 100$

$W = p \cdot (650 - 2 \cdot p) - 20 \cdot (650 - 2 \cdot p)$

Exercise 2

In these formulas express $y$ in $x$ . After that, write them in their simplest form.

$x - 2 y = 10$

$(x + 2) \cdot y = 6$

$x = 4 - y^{2}$

$x \cdot y^{2} = 4$

$0.5 x + 1.5 y = 12$

${(x + y)}^{3} = 8$

$x^{2} - y^{2} = 25$

$2 x^{2} + 4 x y = 100$

Exercise 3

Remove the brackets:

$-2 x (x^{2} + 6 x)$

$-2 x - (x^{2} + 6 x)$

$(t + 20) (t - 5)$

$(x^{2} + 1) (3 x - 2)$

$(a - 3) (a + 3)$

${(6 x - 3)}^{2}$

${(a - \frac{1}{a})}^{2}$

${(x - 2)}^{3}$

Exercise 4

Factorize:

$x^{2} - 4 x$

$- 2 t^{2} + 18 t$

$x^{2} + 5 x - 6$

$12 - 4 p - p^{2}$

$4 k^{2} - 16$

$2 p^{3} - 2 p^{2} - 24 p$

$16 - p^{2}$

$x^{2} - 10 x + 9$

Exercise 5

Write as one fraction (assume you never divide by $0$ ):

$\frac{3}{y} + \frac{5}{x}$

$\frac{3}{x - 2} - \frac{2}{x}$

$\frac{2}{x} / \frac{3}{y}$

$2 x - \frac{1}{2 x}$

Exercise 6

A farmer has a rectangular plot of land with a length of twice its width. From a landscape management point of view he removes a $3$ meter wide strip on both sides and replaces it with a narrow strip of woodland. He also makes a wider strip of woodland of $10$ meters wide at one of the short ends of his plot. As a result the surface area of his land decreases with $2690$ m².

First make a sketch of the situation. The original width of the plot is $x$ (in meter). What is the surface area of this piece of land?

What is the surface area after a part of it has been converted into woodland? (remember the brackets!)

Remove the brackets and calculate the width of the rectangular plot.

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