Lesson 2 · from §25 of the 1910 text
Putting Terms in Parentheses
The principles also run backward: we can put terms into a parenthesis.
16 + 9 - 5 = 16 + (9 - 5) = 16 + 4 = 20, and likewise a + b - c = a + (b - c).
Principle. Terms may be inclosed in a parenthesis preceded by a plus sign without changing any of their signs.
17 + 8 - 3 = 17 - (-8 + 3) = 17 - (-5) = 22, and likewise a + b - c = a - (-b + c).
Principle. Terms may be inclosed in a parenthesis preceded by a minus sign if the sign of each inclosed term is changed.
This is a handy move later, when you start factoring. For example: x^2 - a^2 - 2ab - b^2 = (x^2) - (a^2 + 2ab + b^2)
Quick check
Fill in the parenthesis: p - q + r = p - (\;?\;)
Exercises
How to type math
Use ^ for powers (a^2), / for fractions ((a+b)/2), sqrt(x) for square roots, and cbrt(x) for cube roots. You can leave out the multiplication sign: 3ab means 3 \cdot a \cdot b. Mixed numbers like 4 1/2 work too. The preview under each box shows how your answer was read.
Group the terms.
Write x^2 - a^2 - 2ab - b^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write 12ab + x^2 - 9b^2 - 4a^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write y^2 - 4b^2 + 4ab - a^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write 10ab + x^2 - a^2 - 25b^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write x^2 - b^2 - 4a^2 + 4y^2 - 4ab - 4xy as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write 4ab + x^2 - 4b^2 + y^2 - a^2 - 2xy as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write 16x^2 - a^2 - 16xy - b^2 + 2ab + 4y^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?
Write x^2 - b^2 - 10xy + 12ab - 36a^2 + 25y^2 as (\;\ldots\;) - (\;\ldots\;): the x and y terms inside a parenthesis preceded by +, and the a and b terms inside a parenthesis preceded by -. What goes inside each?