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Algebra Warmups

From cracking cryptograms to calculating the top speed of a rocket, algebra gives you tools to apply mathematical reasoning to a wide range of problems. Dive in and see what you already know!

Algebra Shortcuts Warmup

Evaluate

$\large \frac{ \color{green}{2015} \times \color{blue}{1999} -\color{green}{2015} \times \color{red}{1379}} { \color{blue}{1999} - \color{red}{1379} } .$

Hint: Use the distributive property.

If $$a = 2 , b = 7, c = 9$$, what is the value of

$1 + a + b + c + ab + bc + ca + abc ?$

Hint:

Evaluate

$\Large \color{red}{87} ^ 2 - \color{orange}{86} ^ 2.$

Hint: Use the difference of two squares identity.

$\large \frac {\color{red}6! \times \color{blue}7!}{\color{purple}{10}!} = \ \color{green}?$

Evaluate

$\large \frac{ \color{blue}{42} ^ 2 - \color{green}{38} ^ 2 } { \color{blue}{42} - \color{green}{38} }.$

Hint: Use the difference of two squares identity.

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