Question

The following steps are used to rewrite the polynomial expression (x+2y)(x-5y)

step 1: x(x-5y)+2y(x-5y).
step 2: x^2-5xy+2yx-10y^2.
step 3: x^2-5xy+2xy-10y^2.
step 4: x^2-3xy-10y^2
identify the property used in each of these steps.

Answer 1

1. distributivity of the multiplication (a+b)(c-d)=a(c-d)+b(c-d)
2. the same
3. comutativity of the multiplication a*b=b*a
4. we give common factor xy: -5xy+2xy=xy(-5+2)=-3xy

Answer 2

Explanation:

To multiply two binomials given as

(x+2y)(x-5y)

step 1: x(x-5y)+2y(x-5y). ... Distributive property over multiplication

step 2: x^2-5xy+2yx-10y^2. ... Distributive property over multiplication

step 3: x^2-5xy+2xy-10y^2. ... Commutative property over multiplication

step 4: x^2-3xy-10y^2 ... Simplifying like terms

Thus first we distribute x the first term in the first bracket over the two elements in the second term. Then second term in the first bracket.

Then use commutative property, and simplify like terms

Write answer in descending powers of x and ascending powers of y