Question

which expressions are equivalent to x(5y+60)? Select all that apply. a. (2xy+20x+3xy+40x)b.xy+60xc.y+12xd.25xy+300xe.13yf.x(y+12)

Answer 1

The equivalent expression to x(5y+60) is a. (2xy+20x+3xy+40x), which simplifies to 5xy + 60x after distribution of the x term.

Step-by-step explanation:

To determine which expressions are equivalent to x(5y+60), we should distribute the x across the terms inside the parentheses, resulting in 5xy + 60x.

• Expression a. (2xy+20x+3xy+40x) simplifies to 5xy + 60x, which is equivalent since 2xy + 3xy equals 5xy and 20x + 40x equals 60x.
• Option b. xy + 60x is not equivalent because it lacks the 5 multiplient with xy.
• Option c. y + 12 misses the x variable, therefore, is not equivalent.
• Option d. 25xy + 300x is also not equivalent because the coefficients are five times greater than required.
• Option e. 13y isn't equivalent as it completely lacks the x term and coefficient for y is incorrect.
• The expression f. x(y + 12) upon distribution, results into xy + 12x, which is clearly not equivalent as the coefficients do not match our target expression.

The only equivalent expression to x(5y+60) is a. (2xy+20x+3xy+40x).

Answer 2

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data

x(5y+60)

equivalent expressions = ?

Step 02:

We must apply the algebraic rules to find the solution.

x(5y+60) = 5xy + 60x

a. (2xy+20x+3xy+40x) = 5xy + 60x TRUE

b.xy+60x FALSE

c.y+12x FALSE

d. (25xy+300x) / 5 = 5xy + 60x TRUE

e.13y FALSE

f.x(y+12)​ = xy + 12x FALSE

The answer is:

a. (2xy+20x+3xy+40x) = 5xy + 60x TRUE

d. (25xy+300x) / 5 = 5xy + 60x TRUE