Question

1. simplify the polynomials.

$(3x^{2}+12xy + 5y^{2})(4x - 3y)$
extended foil

combining like terms

side circles, rectangles and underline into like terms.
answer

Explanation:

Step1: Use distributive property (Extended Foil)

$$(3x^{2})(4x)+(3x^{2})(- 3y)+(12xy)(4x)+(12xy)(-3y)+(5y^{2})(4x)+(5y^{2})(-3y)$$

Step2: Calculate each product

$$12x^{3}-9x^{2}y + 48x^{2}y-36xy^{2}+20xy^{2}-15y^{3}$$

Step3: Combine like terms

For \(x^{2}y\) terms: \(-9x^{2}y+48x^{2}y = 39x^{2}y\)
For \(xy^{2}\) terms: \(-36xy^{2}+20xy^{2}=-16xy^{2}\)

Answer:

\(12x^{3}+39x^{2}y - 16xy^{2}-15y^{3}\)