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Answer:
The factorization of is
Step-by-step explanation:
This is a case of factorization by <em>sum and difference of cubes</em>, this type of factorization applies only in binomials of the form or
. It is easy to recognize because the coefficients of the terms are <u><em>perfect cube numbers</em></u> (which means numbers that have exact cubic root, such as 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000, etc.) and the exponents of the letters a and b are multiples of three (such as 3, 6, 9, 12, 15, 18, etc.).
Let's solve the factorization of by using the <em>sum and difference of cubes </em>factorization.
1.) We calculate the cubic root of each term in the equation , and the exponent of the letter x is divided by 3.
then
So, we got that
which has the form of
which means is a <em>sum of cubes.</em>
<em>Sum of cubes</em>
with y
2.) Solving the sum of cubes.
.
Answer:
DE = 6 cm
Step-by-step explanation:
Let DE = x cm.
Since DE is parallel to AB therefore by the alternate interior angles theorem, m∠BAD = m∠ADE and m∠ABE = m∠DEB ............(1)
As AD is an angle bisector of ∠A, therefore m∠EAD = m∠DAB ; Since BE is an angle bisector of ∠B ⇒ m∠ABE = m∠EBD.
Therefore, from (1) We get , m∠EAD = m∠ADE and m∠EBD = m∠BED.
So, the triangles ADE and EDB are then isosceles with AE = ED and ED = DB.
So AE = DE = DB = x, and since the perimeter of ABDE is 30 cm, then
12 + x + x + x = 30
⇒ 12 + 3x = 30
⇒ x = 6
Hence, the length of DE is 6 cm.
