<u>Answer:</u>
<u>(625 • (x4)) - 28y4</u>
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<u> 54x4 - 28y4 3.1 Factoring: 625x4-256y4 </u>
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<u>Theory : A difference of two perfect squares, A2 - B2 can be factored into (A+B) • (A-B)
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<u>Proof : (A+B) • (A-B) =
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<u> A2 - AB + BA - B2 =
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<u> A2 - AB + AB - B2 =
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<u> A2 - B2Note : AB = BA is the commutative property of multiplication.
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<u>Note : - AB + AB equals zero and is therefore eliminated from the expression.
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<u>Check : 625 is the square of 25 </u>
<u>Check : 256 is the square of 16
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<u>Check : x4 is the square of x2 </u>
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<u>Check : y4 is the square of y2 </u>
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<u>Factorization is : (25x2 + 16y2) • (25x2 - 16y2) 3.2 Factoring: 25x2 - 16y2 </u>
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<u>Check : 25 is the square of 5 </u>
<u>Check : 16 is the square of 4
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<u>Check : x2 is the square of x1 </u>
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<u>Check : y2 is the square of y1 </u>
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<u>Factorization is : (5x + 4y) • (5x - 4y)this is the answer: (25x2 + 16y2) •(5x + 4y) • (5x - 4y)</u>
as alternate interior angles;
as vertical angles;
because point H bisects segment DE (given).