Let "p" represent the number of paper clips in a box.  If there are 76 boxes in a case, write an algebraic expression to show the total number of paper clips.

Write an expression for the product of 12 and a number.

Expand the expression using the distributive property. −4(2h+3)

Given Expression:
−4(2h+3)
Distributive law states that the each attribute inside a parenthesis have same right to access the attributes present outside the parenthesis.
Example : a(b + c) Yields ab + ac after distribution.
Hence, By applying the distribution law to −4(2h+3)  becomes:
−4(2h+3)
=
= (-8h) +(-12)
= -8h - 12.
Hence, From Distributive Law the expression −4(2h+3)  becomes -8h -12.

Use the distributive property to expand the expression: 3(t - 2)

Given Expression:
3(t - 2)
Since, it is in the form a(b+ c) we can apply Distributive Law which produces ab+ ac as a result.
*Similarly, by applying the Distributive Law to 3(t - 2) we get:
3(t - 2)
= () - ()
= 3t - 6.
Hence, the expression 3(t - 2) becomes 3t-6 after it's expansion.

Use the distributive property to expand the expression: 2(y + 5x)

Given Expression:
2(y + 5x)
Since, it is in the form of a(b+ c) we can apply distributive law which produces ab+ ac as  a result.
Then, By applying the Distributive Law to 2(y + 5x) we get:
2(y + 5x)
= () + ()
= 2y + 10x.
Hence, the expression 2(y + 5x) becomes 2y + 10x after it's expansion.

Expand the expression. 5(2 - 3y).

Given Expression:
5(2 - 3y).
Since, it is in the form a(b+ c) we can apply Distributive Law which produces ab + ac as a result.
Hence, By applying the Distributive Law  to 5(2 - 3y) we get:
5(2 - 3y)
= () - ()
= 10 - 15y.
Hence, the expression 5(2 - 3y) becomes 10 - 15y after it's expansion.

Expand the expression. 4(x + 4y - 8z)

Given Expression:
4(x + 4y - 8z)
Since, it is of the form a(b+ c+ d), we can apply Distributive Law which produces ab+ ac + ad as result.
Similarly, by applying the distributive law to 4(x + 4y - 8z):
4(x + 4y - 8z)
=() + () + ()
= 4x + 16y -32x.
Hence, the expression 4(x + 4y - 8z): becomes 4x + 16y -32z after it's expansion.

Expand the expression. 5(x - 3)

Given Expression :
5(x - 3)
Since, it is in the form a(b+ c), we can apply Distributive law, that produces ab + ac as a result.
Similarly, By applying the distributive law to 5(x - 3) becomes,
5(x - 3)
= () - ()
= 5x - 15.
Hence, the expression 5(x - 3) becomes 5x - 15 after it's expansion.

Expansion of -8(3a + 5b) yields

Given Expression:
-8(3a + 5b)
Since, it is in the form a(b+ c) we can apply distributive law which produces ab + ac as a result.
Similarly, by applying the Distributive Law, we get:
-8(3a + 5b)
=()+()
= (-24a) + (-40b)
= -24a - 40b.
Hence, the expression -8(3a + 5b) becomes -24a - 40b after it's expansion.

Expand the expression. 2(a + b)

Given Expression:
2(a+ b)
Since, it is in the form a(b+ c) we can apply distributive law which produces ab+ ac as a result.
Similarly, by applying the Distributive law We get:
2(a+ b)
=(2a) + (2b)
= 2a + 2b.
Hence, the expression 2(a+ b)becomes 2a + 2b after it's expansion. 

Expand the expression. 4(7x + 3).

Given Expression :
4(7x + 3)
Since, It is of the form a(b + c), we can apply distributive law which produces ab+ ac.
Then, By applying the distributive law to a  4(7x + 3), becomes
=  ( 47x) + (43)
= 28x +12.
Hence, the expression  4(7x + 3) becomes 28x + 12 after expansion. 

Expand the expression. 5(x + 2)

Given Expression :
5(x+2)
Then, we know distributive law is to be applied in order to remove the parentheses. Hence,
since, a(b + c) gives ab + ac. Similarly,
5(x+2) = 5x + (52)
= 5x + 10.
Hence, we can say that 5(x+2) = 5x + 10. 

Select the expression that contains only like terms.

We were asked to find the expression that contains only like terms. An expression is said to have only like terms if and only if it contains same variables with different coefficients.
let us consider options and verify the expression that it has only like terms.
Option 1 : 8t - 4t
The variables present in the expression is  only 't'. Hence, we can say that it is the required                          expression that has only like terms.
Hence, We can say that 8t-4t is the required expression that has only like terms.

Add the like terms to create an equivalent expression. 12p + p

Since, an expression contains the like terms. let, us try to reduce them using expression evaluation.
Given Expression :
12p + p
Here, the like terms present in the given expression are 12p,p.
Hence, try to evaluate their operation , 12p + p = 13p.
The final expression obtained from 12p + p = 13p

Robin charges his tenants $400 each month to rent his houses plus $600 security deposit. In the new year, the property taxes increased on the area where he rents, so as a result, he must increase the rate of change by $25 to ensure his profits are not harmed. The equation best represents how much his tenants will now have to pay is

Given That :
Rent paid by tenants per month= 400 dollars
Total security deposit per month= 600 dollars
let, there exists x tenants in the house belongs to the owner.
Rate of change made by owner = 25 dollars.
Now, Amount that should be paid by one tenant =  425 dollars.
Amount that should be paid by x tenants   = 425x dollars
Then, total amount paid by the x tenant = y = 425x + 600
The final equation is  y = 425x + 600 

Robert earns $25 per yard he mows in the summer. If he also makes a onetime amount of $100 for babysitting his brother, write an equation that can be used to determine the number of yards (y) he will need to mow to go to Italy for $3,100.

Given That:
Number of yards : y
Amount earned by Robert per yard : 25 dollars
Amount earned by Robert from his brother : 100 dollars
Total amount needed to go to Italy : 3100 dollars.
Hence, Total amount earned by Robert for y yards : 25y dollars
Now, the amount that Robert earn totally = 25y + 100 dollars.
Now, the final Equation becomes 25y + 100 = 3100