Question

For the polynomial below, write down an expression such that if you applied the distributive property to your expression, it would give the result presented.

3x^3 + 6x^4 + 9x^6

Answer 1

The expression to apply distributive property is 3x³ (1+2x²+3x³).

Explanation:

The given polynomial expression is 3x^3 + 6x^4 + 9x^6.

• The distributive property is known as law of multiplication.
• The general form is given by a(b+c) = ab+bc.
• This means that, the outside term must be multiplied with each term inside the bracket.

To transform into distributive form :

• Take x³ outside as a common term,
• The expression becomes x³ (3+6x²+3x³)
• Again taking 3 outside as a common term,
• The expression becomes 3x³ (1+2x²+3x³)

The expression 3x³ (1+2x²+3x³) is equivalent to the given expression 3x^3 + 6x^4 + 9x^6 when distributive property is applied.