Factoring by Short Multiplication - Examples, Exercises and Solutions

Question Types:
Factoring by Short Multiplication: Solving the problem

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:
a2−b2=(a−b)×(a+b)a^2-b^2=(a-b)\times (a+b)

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

a2−2ab+b2=(a−b)2a^2-2ab+b^2=(a-b)^2

Detailed explanation

Practice Factoring by Short Multiplication

Question 1

Find the value of the parameter x.

\( x^2-6x+8=0 \)

Question 2

Find the value of the parameter x.

\( 9x^3-12x^2=0 \)

Question 3

Find the value of the parameter x.

\( -9x+3x^2=0 \)

Question 4

Find the value of the parameter x.

\( x^2+x=0 \)

Examples with solutions for Factoring by Short Multiplication

Exercise #1

Find the value of the parameter x.

x2−6x+8=0 x^2-6x+8=0

Video Solution

Answer

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

Exercise #2

Find the value of the parameter x.

9x3−12x2=0 9x^3-12x^2=0

Video Solution

Answer

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

Exercise #3

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 #4

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

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