Symbolab Algebra Cheat Sheet
Number Rules
• 𝑎 ⋅ 0 = 0 • 1⋅ 𝑎 = 𝑎
Expand Rules
• −(𝑎±𝑏)= −𝑎 ∓ 𝑏
• 𝑎⋅(𝑏+𝑐)⋅(𝑑 + 𝑒)= 𝑎𝑏𝑑 + 𝑎𝑏𝑒 + 𝑎𝑐𝑑 + 𝑎𝑐𝑒
• −(−𝑎)= 𝑎
• 𝑎⋅(𝑏+𝑐)=𝑎𝑏+𝑎𝑐
• (𝑎+𝑏)⋅(𝑐 + 𝑑)=𝑎𝑐 +𝑎𝑑 +𝑏𝑐 +𝑏𝑑
Fraction Rules
• 0
𝑎= 0, 𝑎 ≠ 0
• 𝑎
𝑎= 1
• (𝑎
𝑏)−𝑐 = ((𝑎
𝑏)−1)𝑐= (𝑏
𝑎)𝑐
• 𝑎−𝑏 =1
𝑎𝑏
• −𝑎
𝑏= −𝑎
𝑏
• 𝑎
(𝑏
𝑐)=𝑎⋅𝑐
𝑏
• 1
(𝑏
𝑐)=𝑐
𝑏
• 𝑎
1= 𝑎
• (𝑎
𝑏)−1 =1
(𝑎
𝑏)=𝑏
𝑎
• 𝑎−1 =1
𝑎
• −𝑎
−𝑏 =𝑎
𝑏
• 𝑎
−𝑏 = −𝑎
𝑏
• (𝑏
𝑐)
𝑎=𝑏
𝑐⋅𝑎
Absolute Rules
• |−𝑎|= 𝑎, 0 ≤ 𝑎
• |−𝑎|=|𝑎|
• |𝑎|= 𝑎, 0 ≤ 𝑎
• |𝑎⋅𝑥|= 𝑎 ⋅|𝑥|, 0 ≤ 𝑎
Exponent Rules
• 1𝑎= 1
• 𝑎0= 1, 𝑎 ≠ 0
• (𝑎𝑏)𝑛= 𝑎𝑛𝑏𝑛
• 𝑎𝑚
𝑎𝑛=1
𝑎𝑛−𝑚 , 𝑚 < 𝑛
• (𝑎𝑏)𝑐= 𝑎𝑏⋅𝑐
• (𝑎
𝑏)𝑐=𝑎𝑐
𝑏𝑐
• 𝑎𝑐⋅𝑏𝑐=(𝑎 ⋅𝑏)𝑐
• √𝑎 ⋅ 𝑏
𝑛=√𝑎
𝑛⋅√𝑏
𝑛
• 𝑎1= 𝑎
• 0𝑎= 0, 𝑎 ≠ 0
• 𝑎𝑚
𝑎𝑛= 𝑎𝑚−𝑛, 𝑛 < 𝑚
• 𝑎𝑏+𝑐 = 𝑎𝑏⋅ 𝑎𝑐
• 𝑎𝑏⋅𝑐 =(𝑎𝑏)𝑐
• 𝑎𝑚
𝑛= (√𝑎
𝑛)𝑚
