Factoring Binomials Using The Difference Of Squares - Tiger Algebra

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Camera Icon Enter an equation or problemClear Camera Icon Solve Camera input is not recognized!Keyboardarrow leftarrow rightenterdelsquare 2square 10axy/|abs|( )789*fractionsqrt root456-root%123+<>0,.=abcabcdefghijklmnopqrstuvwxyz␣.Solution - Factoring binomials using the difference of squares 2a3b9c2⋅(4a3+3c2) 2a^3b^9c^2*(4a^3+3c^2)

Other Ways to Solve

Factoring binomials using the difference of squares

Step by Step Solution

Step 1 :

Equation at the end of step 1 :

(((8•(a6))•(b9))•(c2))+(((2•3a3)•b9)•c4)

Step 2 :

Equation at the end of step 2 :

((23a6 • b9) • c2) + (2•3a3b9c4)

Step 3 :

Step 4 :

Pulling out like terms :

4.1 Pull out like factors : 8a6b9c2 + 6a3b9c4 = 2a3b9c2 • (4a3 + 3c2)

Trying to factor as a Sum of Cubes :

4.2 Factoring: 4a3 + 3c2 Theory : A sum of two perfect cubes, a3 + b3 can be factored into : (a+b) • (a2-ab+b2)Proof : (a+b) • (a2-ab+b2) = a3-a2b+ab2+ba2-b2a+b3 = a3+(a2b-ba2)+(ab2-b2a)+b3= a3+0+0+b3= a3+b3Check : 4 is not a cube !! Ruling : Binomial can not be factored as the difference of two perfect cubes

Final result :

2a3b9c2 • (4a3 + 3c2)

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Why learn this

Terms and topics

  • Factoring binomials as sum or difference of cubes
  • Pulling out like terms

Related links

  • Beginning Algebra Tutorial 11: Simplifying Algebraic Expressions

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