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use mathematical properties to create two expressions that are equivalent to the expression: 8(3j + 7 + 3j)
use either the commutative property or combine like terms to create an equivalent expression.

make sure you show all steps in your work .

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Please look at the steps below.

Step-by-step explanation:

1) m∠BAC=m∠CAD,   m∠ACB=m∠ADC=90 degrees , then  m<ABC=m∠ACD.

Therefore, triangles ADC and ACB are similary by AAA theorem.

2)AC /AB = AD/AC

3) Substituting the lengths, we get b/c = e/b

4) Cross multiplying the ratio, we get b^2 = ce

5)  m∠ABC=m∠CBD, m∠ACB=m∠CDB=9, then  m∠BAC=m∠BCD  and the triangles BDC and BCA are similar by AAA theorem.

6)  The ratio of the corresponding sides of similar triangles is in proportion.

BC/BD = AB/BC

7) Substituting the lengths, we get a/d = c/a

8) a^2 = cd

9) Add the results in 4) and 8), we get b^2 + a^2 = ce + cd

10) b^2 + a^2= c(e + d)

11) e + d =c, when we plug in step 10, we get  a^2 + b^2 = c.c

a^2 + b^2 = c^2.

Hope this will helpful.

Thank you.