Decomposition of factors according to the abbreviated multiplication formulas - Examples, Exercises and Solutions

The formulas for shortened multiplication will help us convert expressions with terms that have among them signs of addition or subtraction into expressions whose terms are multiplied.
The formulas for contracted multiplication are:
a2b2=(ab)×(a+b)a^2-b^2=(a-b)\times (a+b)

a2+2ab+b2=(a+b)2a^2+2ab+b^2=(a+b)^2

a22ab+b2=(ab)2a^2-2ab+b^2=(a-b)^2

To use the first formula: a2b2=(ab)×(a+b) a^2-b^2=(a-b)\times(a+b)

Practice Decomposition of factors according to the abbreviated multiplication formulas

Exercise #1

Find the value of the parameter x.

x2+x=0 x^2+x=0

Video Solution

Answer

x=0,x=1 x=0,x=-1

Exercise #2

Find the value of the parameter x.

9x+3x2=0 -9x+3x^2=0

Video Solution

Answer

x=0,x=3 x=0,x=3

Exercise #3

Find the value of the parameter x.

9x312x2=0 9x^3-12x^2=0

Video Solution

Answer

x=0,x=43 x=0,x=\frac{4}{3}

Exercise #4

Find the value of the parameter x.

x26x+8=0 x^2-6x+8=0

Video Solution

Answer

x=2,x=4 x=2,x=4

Topics learned in later sections

  1. Factorization
  2. Extracting the common factor in parentheses
  3. Factorization: Common factor extraction
  4. Factoring Trinomials
  5. Algebraic Fractions
  6. Simplifying Algebraic Fractions
  7. Factoring Algebraic Fractions
  8. Addition and Subtraction of Algebraic Fractions
  9. Multiplication and Division of Algebraic Fractions
  10. Solving Equations by Factoring
  11. Uses of Factorization