Can you factor 4c^8 + 9d^2

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24-09-2016
Mathematics

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Can you factor 4c^8 + 9d^2

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Аноним Аноним · Answer 1 · 2016-09-25T18:03:09+02:00

4c2-9d2 Final result : (2c + 3d) • (2c - 3d) Step by step solution :Step 1 :Skip Ad
Equation at the end of step 1 : (4 • (c2)) - 32d2 Step 2 :Equation at the end of step 2 : 22c2 - 32d2 Step 3 :Trying to factor as a Difference of Squares :

3.1      Factoring:  4c2-9d2

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 - B2

Note :  AB = BA is the commutative property of multiplication.

Note :  - AB + AB equals zero and is therefore eliminated from the expression.

Check :  4  is the square of   2
Check : 9 is the square of 3
Check :  c2  is the square of   c1

Check :  d2  is the square of   d1

Factorization is :       (2c + 3d)  •  (2c - 3d)

Final result : (2c + 3d) • (2c - 3d)

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