Simplifying by Adding or Subtracting Common Radical Factors
A new guideline for simplifying radicals is introduced: the terms in a fully-simplified radical expression must have no common radical factors. Simplifying a radical expression by adding or subtracting common radical factors is illustrated.
Subject: add
Transcript: GREATEST COMMON FACTOR. THE REMAINING FACTOR, 3 PLUS 4, EQUALS 7. SO 3A PLUS 4A EQUALS 7A. WE USUALLY SKIP THE MIDDLE STEP. WE ADD THE COEFFICIENTS WHEN THE
Simplifying to Find a Common Radical Factor
The process of simplifying to find a common radical factor is demonstrated.
Subject: add
Transcript: TIMES THE SQUARE ROOT OF 6. NOW WE HAVE TWO TERMS WITH A COMMON FACTOR. WE'LL ADD THE COEFFICIENTS TO GET 5 TIMES THE SQUARE ROOT OF 6. IN THIS PROBLEM
Practical Problem: Subtracting Boxes in a Warehouse
A practical problem solved using subtraction in an algebraic expression.
Subject: add
Polynomials, Monomials, Binomials, Trinomials
Three types of polynomials are defined: monomials, binomials, and trinomials.
Subject: add
Transcript: NARRATOR: ALL WE'VE DONE WITH THE VARIABLES IS ADD, SUBTRACT, AND MULTIPLY THEM, OR RAISE THEM TO A POWER. NO DIVIDING BY VARIABLES. NO VARIABLES
Subtracting Like Terms
Subtracting like terms demonstrated and applied to a practical problem.
Subject: add
Summary of the Addition of Like Terms
Review and practice of adding terms in a simple algebraic expression.
Subject: add
Transcript: NARRATOR: TO ADD TWO OR MORE TERMS, FIRST, SEE IF THEY ARE LIKE TERMS. IF NOT, JUST COPY THEM OVER. THERE IS NOTHING MORE YOU CAN DO. IF YOU FIND
Solving an Equation by Multiplying
An explanation of how to solve an algebraic equation by adding.
Subject: add
Transcript: MINUS A CONSTANT, WE GET RID OF THE CONSTANT BY ADDING IT TO BOTH SIDES OF THE EQUATION. FIRST, WE ADD 7 TO X MINUS 7. THAT GIVES US JUST WHAT WE WANT, X
Summary of the Order of Operations and Use of Parentheses in Algebra
The standard order of operations and the use of parentheses in Algebra are summarized.
Subject: add
Transcript: LEFT. THIRD, ADD OR SUBTRACT. AS BEFORE, WE START AT THE LEFT. THESE RULES ARE KNOWN AS THE STANDARD ORDER OF OPERATIONS. WHEN WE EXAMINE AN EXPRESSION
Rules for Subtracting Algebraic Expressions
Rules for subtracting one algebraic expression from another and a step-by-step demonstration.
Subject: add
Transcript: 'RE ADDING THOSE TWO NEW TERMS. WE KNOW HOW TO ADD, WE JUST COMBINE LIKE TERMS. WE HAVE 10AB MINUS 3AB. THAT GIVES US 7AB. ARE THERE ANY MORE? YES, 6C MINUS 2C
Solving Systems of Equations Using the Elimination Method by Adding
Explanation of the elimination method of solving a system of equations. Adding the equations to eliminate a variable is quicker than using the substitution method, but requires that both equations be in the same form and that the system contain an a...
Subject: add
Transcript: NARRATOR: LET'S LOOK AT A DIFFERENT METHOD. WE'LL BEGIN BY ADDING THE FIRST EQUATION TO THE SECOND EQUATION. WE ADD THE EXPRESSIONS ON THE LEFT