Expand the expression. 4(x + 4y - 8z)

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.

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.

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. 

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. 

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. 

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.

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

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 

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

The expression is evaluated using the like terms. Reduce the given expression into a final expression by performing required operations.
Given Expression:
4x² - 3x + 11 - 2x
Here, the like terms are -3x, -2x. Then,
adding like terms : -5x
Final Expression becomes 4x² - 5x +11
* Hence, The final expression becomes 4x² -5x +11.

Since, an expression can have any terms in it. we can reduce the like terms with the operation between them and combine their results to obtain the final expression.
Given Expression:
3 + 5x + 8 – 2x
Here, the like terms are 3,5 with 0 degree terms and 5x, -2x with 1 degree terms. Then,
**degree 0 terms>> 3+8 = 11
degree 1 terms >>5x-2x = 3x
** By combining the above results gives 3x + 11
Hence, an expression becomes  3 + 5x + 8 – 2x = 11 + 3x.

Since, expression is evaluated with the reduction of like terms and combining their results to get the final expression.
Given Expression;
3x + 1 + 7x.
Here, the like terms are 3x, 7x. Hence, perform the operation between them
= 10x +1
* Hence, The final expression that we got after the reduction of the like terms is 10x +1.

An expression is having only like terms if and only if it's expression is having only one variable with different coefficients.
Then. let us consider the options to find the expression with like terms.
option 1: 4t - 4t is an expression having only one variable t. Hence, we can say that this is the expression that has only like terms.
***Hence, we can say that 4t-4t is the expression that has only like terms. 

When an expression is said to have only like terms if it's expression has only one variable with different coefficients.
Given that:
we were asked to find the expression having only terms.
Hence, let us consider first option 15k + 2k - 4k + 2 , it has k, 2 as variable terms. Hence, It is having unlike terms.
Similarly, second Option:   16h - 7h + 3g - 9h, it has variables g, h . Hence, it is having unlike terms.
Similarly, Third option : 5r - 3r + 6r - r, it has only one variable r. Hence, it is considered as the expression having only like terms.

Since, the given expression is reduced to solve using the like terms present in the expression.
Given that:
5p + 7y + 2t - 3p + 4y
Like terms presents in the expression are 5p, -3p and 7y, 4y.
Hence, 5p + 7y + 2t - 3p + 4y becomes:
= (5p-3p) + (7y+4y) + 2t
= 2p + 11y + 2t
Therefore, 5p + 7y + 2t - 3p + 4y = 2p + 11y +2t