Question

What must be added to 6a-4b+3c
to produce
2a+3b -5c
?​

Answer 1

If we want to multiply a sum by another number, either we can multiply each term of the sum by the number before we add or we can first add the terms and then multiply. For example,

In either case the result is the same.

This property, which we first introduced in Section 1.8, is called the distributive law. In symbols,

a(b + c) = ab + ac or (b + c)a = ba + ca

By applying the distributive law to algebraic expressions containing parentheses, we can obtain equivalent expressions without parentheses.

Our first example involves the product of a monomial and binomial.

Example 1 Write 2x(x - 3) without parentheses.

Answer 2

Answer:

-4a+7b-8c

Step-by-step explanation:

(6a-4b+3c) + ? = (2a+3b-5c)

Therefore, ? = (2a+3b-5c) - (6a-4b+3c)

                     = (-4a+7b-8c)