Solve Factoringbinomialsasdifferenceofsquares 4x^2=484 Tiger ...

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Enter an equation or problemClear Solve × Camera input is not recognized!axy/|abs|( )789*456-%123+<>0,.=abcabcdefghijklmnopqrstuvwxyz␣.Solution - Factoring binomials using the difference of squares x=11 x=11 x=−11 x=-11

Other Ways to Solve

Factoring binomials using the difference of squares

• Solving quadratic equations by factoring
• Solving quadratic equations using the quadratic formula
• Solving quadratic equations by completing the square

Step by Step Solution

Rearrange:

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation : 4*x^2-(484)=0

Step by step solution :

Step 1 :

Equation at the end of step 1 :

22x2 - 484 = 0

Step 2 :

Step 3 :

Pulling out like terms :

3.1 Pull out like factors : 4x2 - 484 = 4 • (x2 - 121)

Trying to factor as a Difference of Squares :

3.2 Factoring: x2 - 121 Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)Proof : (A+B) • (A-B) = A2 - AB + BA - B2 = A2 - AB + AB - B2 = A2 - B2Note : AB = BA is the commutative property of multiplication. Note : - AB + AB equals zero and is therefore eliminated from the expression.Check : 121 is the square of 11Check : x2 is the square of x1 Factorization is : (x + 11) • (x - 11)

Equation at the end of step 3 :

4 • (x + 11) • (x - 11) = 0

Step 4 :

Theory - Roots of a product :

4.1 A product of several terms equals zero.When a product of two or more terms equals zero, then at least one of the terms must be zero.We shall now solve each term = 0 separatelyIn other words, we are going to solve as many equations as there are terms in the productAny solution of term = 0 solves product = 0 as well.

Equations which are never true :

4.2 Solve : 4 = 0This equation has no solution. A a non-zero constant never equals zero.

Solving a Single Variable Equation :

4.3 Solve : x+11 = 0Subtract 11 from both sides of the equation : x = -11

Solving a Single Variable Equation :

4.4 Solve : x-11 = 0Add 11 to both sides of the equation : x = 11

Two solutions were found :

1. x = 11
2. x = -11

How did we do?

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Why learn this

Terms and topics

• Factoring binomials as difference of squares
• Linear equations with one unknown

Related links

• How to Factor the Difference of Two Perfect Squares
• Alg 21 - math homework help – math tutor software

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