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mash [69]
3 years ago
14

Factor the expression completely. 625x4 - 256y4

Mathematics
1 answer:
scoundrel [369]3 years ago
5 0

<u>Answer:</u>

<u>(625 • (x4)) -  28y4</u>

<u></u>

<u>  54x4 -  28y4 3.1      Factoring:  625x4-256y4  </u>

<u> </u>

<u>Theory : A difference of two perfect squares,  A2 - B2  can be factored into  (A+B) • (A-B) </u>

<u> </u>

<u>Proof :  (A+B) • (A-B) = </u>

<u>         A2 - AB + BA - B2 = </u>

<u>         A2 - AB + AB - B2 = </u>

<u>         A2 - B2Note :  AB = BA is the commutative property of multiplication. </u>

<u> </u>

<u>Note :  - AB + AB equals zero and is therefore eliminated from the expression. </u>

<u> </u>

<u>Check :  625  is the square of  25  </u>

<u>Check : 256 is the square of 16 </u>

<u>Check :  x4  is the square of  x2  </u>

<u> </u>

<u>Check :  y4  is the square of  y2  </u>

<u> </u>

<u>Factorization is :       (25x2 + 16y2)  •  (25x2 - 16y2)  3.2      Factoring:  25x2 - 16y2  </u>

<u> </u>

<u>Check :  25  is the square of  5  </u>

<u>Check : 16 is the square of 4 </u>

<u>Check :  x2  is the square of  x1  </u>

<u> </u>

<u>Check :  y2  is the square of  y1  </u>

<u> </u>

<u>Factorization is :       (5x + 4y)  •  (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)</u>

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