Math

QuestionWhich option shows the associative property of addition? a. (1+3)2+7=1+(3+7)2(1+\sqrt{3})^{2}+\sqrt{7}=1+(\sqrt{3}+\sqrt{7})^{2} b. (2+7i)+4i=2+(7i+4i)(-2+7 i)+4 i=-2+(7 i+4 i) c. 18+53(6+5)\sqrt{18}+5 \sqrt{3}(\sqrt{6}+5) d. (5i2i)+11i=11i+(5i2i)(5 i \cdot 2 i)+11 i=11 i+(5 i \cdot 2 i)

Studdy Solution

STEP 1

Assumptions1. The associative property of addition states that for all real numbers a, b, and c, the equation (a + b) + c = a + (b + c) holds true. . The options given are mathematical expressions that need to be evaluated to see if they follow the associative property of addition.

STEP 2

Evaluate option a.
(1+)2+7=1+(+7)2 (1+\sqrt{})^{2}+\sqrt{7}=1+(\sqrt{}+\sqrt{7})^{2} This statement does not illustrate the associative property of addition. It seems to be more related to the distributive property, as it involves the square of a sum.

STEP 3

Evaluate option b.
(2+7i)+i=2+(7i+i) (-2+7 i)+ i=-2+(7 i+ i) This statement is an illustration of the associative property of addition. In this case, a = -2, b =7i, and c =i. The equation shows that (-2 +7i) +i = -2 + (7i +i), which follows the form (a + b) + c = a + (b + c).

STEP 4

Evaluate option c.
18+3(6+) \sqrt{18}+ \sqrt{3}(\sqrt{6}+) This statement does not illustrate the associative property of addition. It seems to be more related to the distributive property, as it involves the multiplication of a sum by a number.

STEP 5

Evaluate option d.
(5i2i)+11i=11i+(5i2i) (5 i \cdot2 i)+11 i=11 i+(5 i \cdot2 i) This statement does not illustrate the associative property of addition. It seems to be more related to the commutative property, as it involves the rearrangement of terms.

STEP 6

After evaluating all the options, we can conclude that option b is the one that illustrates the associative property of addition.
So, the answer is option b (2+i)+4i=2+(i+4i)(-2+ i)+4 i=-2+( i+4 i).

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