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Use the distributive property (and your wits!) to write each of the following expressions as a sum of monomials. If the resulting polynomial is in one variable, write the polynomial in standard form.

(a+b)^2 (a+1)^2 (3+b)^2

(3+1)^2 (x+y+z)^2 (x+1+z)^2

(3+z)^2 (p+q)^3 (p-1)^3

(5+q)^3

Respuesta :

MrRoyal

The simplified expressions are (2a + 2b + 4)^2, (5 + 2x + y + 2z)^2, (3 + z)^2 (2p + q - 1)^3 and (5+q)^3

How to apply the distributive property?

The distributive property states that:

a^x * b^x = (ab)^x

So, we have:

(a+b)^2 (a+1)^2 (3+b)^2

(a+b)^2 (a+1)^2 (3+b)^2 = (a + b + a + 1 + 3 + b)^2

Evaluate the like terms

(a+b)^2 (a+1)^2 (3+b)^2 = (2a + 2b + 4)^2

(3+1)^2 (x+y+z)^2 (x+1+z)^2

(3+1)^2 (x+y+z)^2 (x+1+z)^2 = (3 + 1 + x + y + z + x + 1 + z)^2

Evaluate the like terms

(3+1)^2 (x+y+z)^2 (x+1+z)^2 = (5 + 2x + y + 2z)^2

(3+z)^2 (p+q)^3 (p-1)^3

(3+z)^2 (p+q)^3 (p-1)^3 = (3 + z)^2 (p + q + p - 1)^3

Evaluate the like terms

(3+z)^2 (p+q)^3 (p-1)^3 = (3 + z)^2 (2p + q - 1)^3

(5+q)^3

This cannot be further expanded

Read more about polynomials at:

https://brainly.com/question/4142886

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