QuestionRewrite and simplify using the Distributive Property:
23. $2(x+4)$ , 24. $(5+n) 3$ , 25. $(4-3 m) 8$ , 26. $-3(2 x-6)$ , 27. $(2-4 n) 17$ , 28. $11(4 d+6)$ , 29. $\left(\frac{1}{3}-2 b\right) 27$ , 30. $4(8 p+16 q-7 r)$ , 31. $6\left(2 c-c d^{2}+d\right)$ , 32. $7(h-10)$ , 33. $3(m+n)$ , 34. $2(x-y+1)$ , 35. $\left(\frac{1}{2}+6 a\right) 14$ , 36. $-2(7 m-8 n-5 p)$ , 37. $(0.3-6 x) 9$ , 38. $-4\left(4 a+2 b-\frac{1}{2} c\right)$ .

Studdy Solution

STEP 1

Assumptions1. We are given several expressions that we need to simplify using the Distributive Property. . The Distributive Property states that for all real numbers a, b, and c, a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

Let's start with the first expression, $2(x+4)$ . According to the Distributive Property, we can distribute the2 to both x and4.
$2(x+4) =2x +2*4$

STEP 3

implify the expression.
$2(x+) =2x +8$

STEP 4

Next, let's simplify the second expression, $(+n)3$ . We can distribute the3 to both and n.
$(+n)3 =3* +3n$

STEP 5

implify the expression.
$(5+n)3 =15 +3n$

STEP 6

Next, let's simplify the third expression, $(4-3 m)8$ . We can distribute the8 to both4 and -3m.
$(4-3 m)8 =84 -83m$

STEP 7

implify the expression.
$(4-3 m) =32 -24m$

STEP 8

Next, let's simplify the fourth expression, $-3(2 x-6)$ . We can distribute the -3 to both2x and -6.
$-3(2 x-6) = -32x +36$

STEP 9

implify the expression.
$-3(2 x-6) = -6x +18$

STEP 10

Continue this process for the remaining expressions. The Distributive Property allows us to distribute the number outside the parentheses to each term inside the parentheses. After distributing, simplify the expression by performing the multiplication.

Was this helpful?

Studdy Solution

STEP 1

Assumptions1. We are given several expressions that we need to simplify using the Distributive Property. . The Distributive Property states that for all real numbers a, b, and c, a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

Let's start with the first expression, $2(x+4)$ . According to the Distributive Property, we can distribute the2 to both x and4.
$2(x+4) =2x +2*4$

STEP 3

implify the expression.
$2(x+) =2x +8$

STEP 4

Next, let's simplify the second expression, $(+n)3$ . We can distribute the3 to both and n.
$(+n)3 =3* +3n$

STEP 5

implify the expression.
$(5+n)3 =15 +3n$

STEP 6

Next, let's simplify the third expression, $(4-3 m)8$ . We can distribute the8 to both4 and -3m.
$(4-3 m)8 =84 -83m$

STEP 7

implify the expression.
$(4-3 m) =32 -24m$

STEP 8

Next, let's simplify the fourth expression, $-3(2 x-6)$ . We can distribute the -3 to both2x and -6.
$-3(2 x-6) = -32x +36$

STEP 9

implify the expression.
$-3(2 x-6) = -6x +18$

STEP 10

Continue this process for the remaining expressions. The Distributive Property allows us to distribute the number outside the parentheses to each term inside the parentheses. After distributing, simplify the expression by performing the multiplication.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Studdy Solution

STEP 1

Assumptions1. We are given several expressions that we need to simplify using the Distributive Property. . The Distributive Property states that for all real numbers a, b, and c, a(b + c) = ab + ac and a(b - c) = ab - ac.

STEP 2

Let's start with the first expression, 2(x+4)2(x+4)2(x+4). According to the Distributive Property, we can distribute the2 to both x and4.2(x+4)=2x+2∗42(x+4) =2x +2*42(x+4)=2x+2∗4

STEP 3

implify the expression.2(x+)=2x+82(x+) =2x +82(x+)=2x+8

STEP 4

Next, let's simplify the second expression, (+n)3(+n)3(+n)3. We can distribute the3 to both and n.(+n)3=3∗+3n(+n)3 =3* +3n(+n)3=3∗+3n

STEP 5

implify the expression.(5+n)3=15+3n(5+n)3 =15 +3n(5+n)3=15+3n

STEP 6

Next, let's simplify the third expression, (4−3m)8(4-3 m)8(4−3m)8. We can distribute the8 to both4 and -3m.(4−3m)8=8∗4−8∗3m(4-3 m)8 =8*4 -8*3m(4−3m)8=8∗4−8∗3m

STEP 7

implify the expression.(4−3m)=32−24m(4-3 m) =32 -24m(4−3m)=32−24m

STEP 8

Next, let's simplify the fourth expression, −3(2x−6)-3(2 x-6)−3(2x−6). We can distribute the -3 to both2x and -6.−3(2x−6)=−3∗2x+3∗6-3(2 x-6) = -3*2x +3*6−3(2x−6)=−3∗2x+3∗6

STEP 9

implify the expression.−3(2x−6)=−6x+18-3(2 x-6) = -6x +18−3(2x−6)=−6x+18

STEP 10

Continue this process for the remaining expressions. The Distributive Property allows us to distribute the number outside the parentheses to each term inside the parentheses. After distributing, simplify the expression by performing the multiplication.

Get Studdy

Studdy solves anything!

Start learning now

Download Studdy AI Tutor now. Learn with ease and get all help you need to be successful at school.

Let's start with the first expression, $2(x+4)$ . According to the Distributive Property, we can distribute the2 to both x and4.
$2(x+4) =2x +2*4$

implify the expression.
$2(x+) =2x +8$

Next, let's simplify the second expression, $(+n)3$ . We can distribute the3 to both and n.
$(+n)3 =3* +3n$

implify the expression.
$(5+n)3 =15 +3n$

Next, let's simplify the third expression, $(4-3 m)8$ . We can distribute the8 to both4 and -3m.
$(4-3 m)8 =84 -83m$

implify the expression.
$(4-3 m) =32 -24m$

Next, let's simplify the fourth expression, $-3(2 x-6)$ . We can distribute the -3 to both2x and -6.
$-3(2 x-6) = -32x +36$

implify the expression.
$-3(2 x-6) = -6x +18$