Question

multiply.
(2y - 5x - 1)(5y - 3x + 3)
simplify your answer.

Explanation:

Step1: Apply distributive property (FOIL for trinomials)

Multiply each term in the first trinomial by each term in the second trinomial:
$$(2y - 5x - 1)(5y - 3x + 3)=2y(5y - 3x + 3)-5x(5y - 3x + 3)-1(5y - 3x + 3)$$

Step2: Distribute each term

For \(2y(5y - 3x + 3)\): \(2y\times5y = 10y^{2}\), \(2y\times(-3x)=-6xy\), \(2y\times3 = 6y\)
For \(-5x(5y - 3x + 3)\): \(-5x\times5y=-25xy\), \(-5x\times(-3x)=15x^{2}\), \(-5x\times3=-15x\)
For \(-1(5y - 3x + 3)\): \(-1\times5y=-5y\), \(-1\times(-3x)=3x\), \(-1\times3=-3\)
So we have:
$$10y^{2}-6xy + 6y-25xy+15x^{2}-15x-5y + 3x-3$$

Step3: Combine like terms

• For \(xy\) terms: \(-6xy-25xy=-31xy\)
• For \(y\) terms: \(6y - 5y=y\)
• For \(x\) terms: \(-15x+3x=-12x\)

Now combine all terms:
$$10y^{2}+15x^{2}-31xy + y-12x-3$$

Answer:

\(15x^{2}-31xy + 10y^{2}-12x + y-3\)