Question

matching equivalent expressions

match each expression written in standard form to the equivalent expression in factored form.

1. \\(15x^7y^2 + 3x\\)
2. \\(15x^7y^2 + 6xy\\)
3. \\(15x^7 + 10y^2\\)
4. \\(15x^7y^2 + 4x^3\\)

options:

• \\(3x(5x^6y^2 + 1)\\)
• \\(x^3(15x^4y^2 + 4)\\)
• \\(5(3x^7 + 2y^2)\\)
• \\(3xy(5x^6y + 2)\\)

Explanation:

Factor the first expression

$$ 15x^7y^2 + 3x = 3x(5x^6y^2 + 1) $$

Factor the second expression

$$ 15x^7y^2 + 6xy = 3xy(5x^6y + 2) $$

Factor the third expression

$$ 15x^7 + 10y^2 = 5(3x^7 + 2y^2) $$

Factor the fourth expression

$$ 15x^7y^2 + 4x^3 = x^3(15x^4y^2 + 4) $$

Answer:

Standard Form	Factored Form
\(15x^7y^2 + 6xy\)	\(3xy(5x^6y + 2)\)
\(15x^7 + 10y^2\)	\(5(3x^7 + 2y^2)\)
\(15x^7y^2 + 4x^3\)	\(x^3(15x^4y^2 + 4)\)