FORMULABANK

Plus Parentheses

When there is a plus sign or no sign in front of the parentheses.
A plus parentheses can be removed without making any changes.

Example:
(2a + 3) + (4a + 2) = 2a + 3 + 4a + 2

Minus Parentheses

When there is a minus sign in front of the parentheses. (Highlighted in yellow)
A minus parentheses is removed by changing the sign of all terms inside the parentheses, and the minus sign in front is dropped. (Changed signs are shown in green)
Example:
(2a + 3) - (-4a + 2) = 2a + 3 + 4a - 2

Multiplying into Parentheses

Multiply each term inside the parentheses.
Example:
2·(2a + b) = 2·2a + 2·b = 4a + 2b

Dividing a Parentheses by a Number

Divide each term inside the parentheses by the number.

Example:
$\frac{(4a+2b)}{2}=\frac{4a}{2}+\frac{2b}{2}=2a+b$

Square Sentences

The Square of a Binomial Sum

Formula:
$(a+b)2^{}=a^2+b^2+2ab$

Calculation:
$(a+b)2^{}=(a+b)\cdot (a+b)=(a\cdot a)+(a\cdot b)+(b\cdot a)+(b\cdot b)=a^2+b^2+2ab$

The Square of a Binomial Difference

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

Calculation:
$(a-b)2^{}=(a+b)\cdot (a-b)=(a\cdot a)+(a\cdot \mathrm{-b})+(\mathrm{-b}\cdot a)+(\mathrm{-b}\cdot \mathrm{-b})=a^2+b^2-2ab$

Sum of Two Terms Multiplied by Their Difference

Formula:
$(a+b)\cdot (a-b)=a^2-b^2$

Calculation:
$(a+b)\cdot (a-b)=(a\cdot a)+(a\cdot \mathrm{-b})+(b\cdot a)+(\mathrm{-b}\cdot \mathrm{-b})=a^2-b^2$