Algebra: Chapter 5, Lesson 11, page 249.
Multiplying Polynomials
To multiply a monomial and a polynomial: multiply each term of the polynomial by the monomial
There are 3 techniques to multiply binomials:
- FOIL (FIRST, OUTSIDE, INSIDE, LAST – or its derivatives for trinomials)
- Multiply each term of a polynomial by EVERY OTHER TERM of the other polynomial
- The BOX method
- The BOX method, more like a rectangle with each term representing 1 side of an inner box. A binomial multiplied with a trinomial will be a BOX containing 2 x 3 number of smaller boxes inside it. Each term represents 1 edge in distance in the inner boxes.
- The old fashioned multiplication method outlined on page 249.
You get to chose which is most comfortable for you BUT REMEMBER THE BOX for Chapter 6!
Remember too, the shortcuts for special binomials:
- `(A+B)(A+B)=(A+B)^2=A^2+B^2+2AB`
- `(A−B)(A−B)=(A−B)2=A^2+B^2−2AB`
- `(A+B)(A−B)=A^2−B^2`
Two of tonight’s homework problems solved by MrE are here! Just click it!
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Algebra 1a: Chapter 4, Review for TOMORROW’s 200 POINT BENCHMARK!
Chapter Review – 2 Step Equations & Inequalities
Follow these steps and you can’t go wrong … take your time!
- If you have an absolute value, `|x|` for the variable, remove it (ignore it) and rewrite as if it didn’t exist.
- Multiply both sides to clear fractions or decimals, if necessary. Multiply by the LCD for fractions or by `10` or `100` for decimals.
- Distribute (whacky arrows) if you see parenthesis `( )` or square brackets `[ ]`
- Collect like terms on each side, if necessary.
- Use the addition or subtraction property to move the variable to one side and all other terms and constants to the other side of the equation.
- Use the multiplication or division or reciprocal (good for fractions) properties to solve for the variable.
- ONLY FOR INEQUALITIES – if you multiply or divide by a negative number in step 6, DON’T FORGET TO FLIP THE SIGN OF THE INEQUALITY!
- If this was an absolute value problem `|x|`, re-insert the absolute value and check your answers, there may be 2 of them (`±`).
Word Problem Tips
Addition: plus, sum, more than, increased by, total, in all
Subtraction: minus, difference, less than, subtract, decreased by
Multiplication: times, product, multiplied, each, of
Division: dividend, quotient