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:
$a^2-b^2=(a-b)\times (a+b)$

$a^2+2ab+b^2=(a+b)^2$

$a^2-2ab+b^2=(a-b)^2$

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

Detailed explanation

Practice Decomposition of factors according to the abbreviated multiplication formulas

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 decomposition of factors according to the abbreviated multiplication formulas

Exercise #1

Find the value of the parameter x.

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

Video Solution

Answer

$x=2,x=4$

Exercise #2

Find the value of the parameter x.

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

Video Solution

Answer

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

Exercise #3

Find the value of the parameter x.

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

Video Solution

Answer

$x=0,x=3$

Exercise #4

Find the value of the parameter x.

$x^2+x=0$

Video Solution

Answer

$x=0,x=-1$

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

To use the first formula: a2−b2=(a−b)×(a+b) a^2-b^2=(a-b)\times(a+b) a2−b2=(a−b)×(a+b)

Practice Decomposition of factors according to the abbreviated multiplication formulas

examples with solutions for decomposition of factors according to the abbreviated multiplication formulas

Exercise #1

Video Solution

Answer

Exercise #2

Video Solution

Answer

Exercise #3

Video Solution

Answer

Exercise #4

Video Solution

Answer

Topics learned in later sections

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