MTH405_Wk_3_Lect_1 - MTH405 Wk 3 Lect 1 Algebra Denitions...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: MTH405 Wk 3 Lect 1 Algebra Denitions • Variable - the letters x, y and z which has the freedom to represent any number. • Coecient - A number multiplied to a variable. • Term - a group of coecients and variables multiplied or divided to each other. A term is separated from another term by + or − symbols. • Expression - A group of terms added or subtracted together. • Constant - A term which has only a number. • Equation - An expression which is equal to some value. Exercise. 5. Give examples of the following from the equation xy 2 +3y+5xy+23 = 1. Variable 2. Coecient 3. Term 4. Constant 5. Expression 1 Bracket Expansion Rule: When expanding brackets, the term outside is multiplied to every term inside the bracket. Exercise. Expand all the brackets of the following expressions. 1. (x + 2y) + (2x − y) 2. 2(x − y) − 3(y − x) 3. 2(p + 3q − r) − 4(r − q + 2p) + p 4. (a + b)(a + 2b) 5. (p + q)(3p − 2q) Evaluation of Expressions (Substitution) Exercise. Evaluate the following expressions. 1. Find the value of 2xy + 3yz − xyz , when x = 2, y = −2 and z = 4. 2. Evaluate 3pq 3 r3 when p = 23 , q = −2 and r = −1. 3. Find the sum of 3a, −2a, −6a, 5a and 4a. Simplifying Expressions Exercise. Simplify the following expressions. 1. Add together 2a + 3b + 4c, −5a − 2b + c and 4a − 5b − 6c. 2. Add together 3d + 4e, −2e + f , 2d − 3f , 4d − e + 2f − 3e. 3. From 4x − 3y + 2z , subtract x + 2y − 3z . 4. Subtract 23 a − 3b + c from b 2 − 4a − 3c. 5. Simplify (x2 y 3 z)(x3 yz 2 ) and evaluate when x = 12 , y = 2 and z = 3. 6. Simplify (a 2 bc−3 )(a 2 bc− 2 c) and evaluate when a = 3, b = 4 and c = 2. 3 7. Simplify a5 bc3 a2 b3 c2 1 1 and evaluate when a = 32 , b = 2 1 2 and c = 32 . Factorization There are 6 method of factorization. • Common factor • Factorization by Grouping • Type I factorization • Type II factorization • Dierence of Squares • Perfect Square Example. Factorize the following expressions. 1. 3a + 3b 2. 12b2 c3 − 8bc. 3. ax + bx + ay + by 4. x2 + 5x + 4 5. x2 + 7x + 12 6. 2x2 + 10x + 12 7. x2 − 9 8. x2 − 16 Solutions. 1. 3a + 3b = 3(a + b) (Common factor) 2. 12b2 c3 − 8bc = 4bc(3bc2 − 2). (Common factor) 3. ax + bx + ay + by = x(a + b) + y(a + b) = (a + b)(x + y). (Grouping) 4. x2 + 5x + 4 = (x + 4)(x + 1) (Type I) 5. x2 + 7x + 12 = (x + 3)(x + 4) (Type I) 6. 2x2 + 10x + 12 = 2x2 + 4x+ 6x+ 12 = 2x(x + 2) + 6(x + 2) = (x+ 2)(2x+ 6) (Type II Factorization) 7. x2 − 9 = (x + 3)(x − 3) (Dierence of Squares) 8. x2 − 16 = (x − 4)(x + 4) (Dierence of Squares) 3...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern