Question

multiply.

• 4xy(5x + y)
• 4xy(5x + y) = \square (simplify your answer.)

Explanation:

Step1: Apply distributive property

Using the distributive property \(a(b + c)=ab+ac\), here \(a = - 4xy\), \(b = 5x\) and \(c = y\). So we have \(-4xy\times5x+(-4xy)\times y\).

Step2: Multiply the coefficients and variables

For the first term: \(-4\times5\times x\times x\times y=-20x^{2}y\) (using the rule \(x^m\times x^n=x^{m + n}\), here \(m = 1\), \(n = 1\) for \(x\)). For the second term: \(-4\times x\times y\times y=-4xy^{2}\) (using the rule \(y^m\times y^n=y^{m + n}\), here \(m = 1\), \(n = 1\) for \(y\)).

Step3: Combine the terms

Combine the two terms we got: \(-20x^{2}y-4xy^{2}\)

Answer:

\(-20x^{2}y - 4xy^{2}\)