Math

QuestionSimplify the expression: 9(7k+8)+3(k10)9(7k + 8) + 3(k - 10).

Studdy Solution

STEP 1

Assumptions1. We are given the expression 9(7k+8)+3(k10)9(7 k+8)+3(k-10). We need to simplify this expression

STEP 2

First, we apply the distributive property, which states that a(b+c)=ab+aca(b+c) = ab + ac, to the expression 9(7k+8)9(7 k+8).
9(7k+8)=97k+989(7 k+8) =9 \cdot7k +9 \cdot8

STEP 3

Now, we apply the distributive property to the expression 3(k10)3(k-10).
3(k10)=3k3103(k-10) =3 \cdot k -3 \cdot10

STEP 4

Next, we simplify the multiplication in each of the expressions.
97k+98=63k+729 \cdot7k +9 \cdot8 =63k +723k310=3k303 \cdot k -3 \cdot10 =3k -30

STEP 5

Now we combine the two expressions from steps4.
63k+72+3k3063k +72 +3k -30

STEP 6

Next, we combine like terms. Like terms are terms that contain the same variables raised to the same power. In this case, the like terms are 63k63k and 3k3k, and 7272 and 30-30.
63k+3k+723063k +3k +72 -30

STEP 7

Now we add the like terms together.
66k+4266k +42So, the simplified form of the expression 9(7k+)+3(k10)9(7 k+)+3(k-10) is 66k+4266k +42.

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