Question

simplify the following expression. 9r(r + 2s - 9) ?r^ + rs + r

Explanation:

Step1: Apply distributive property

We use the distributive property \(a(b + c + d)=ab+ac + ad\) to expand \(9r(r + 2s-9)\). So we multiply \(9r\) with each term inside the parentheses:

• Multiply \(9r\) and \(r\): \(9r\times r = 9r^{2}\)
• Multiply \(9r\) and \(2s\): \(9r\times2s=18rs\)
• Multiply \(9r\) and \(- 9\): \(9r\times(-9)=- 81r\)

Step2: Match with the given form

The given form is \(\square r^{\square}+\square rs+\square r\). From the expansion:

• For the \(r^{2}\) term, the coefficient is \(9\) and the exponent of \(r\) is \(2\).
• For the \(rs\) term, the coefficient is \(18\).
• For the \(r\) term, the coefficient is \(- 81\).

Answer:

The first box (coefficient of \(r^{2}\)) is \(9\), the exponent of \(r\) is \(2\), the coefficient of \(rs\) is \(18\), and the coefficient of \(r\) is \(-81\). So filling in the boxes: \(9r^{2}+18rs - 81r\) (so the first box is \(9\), exponent of \(r\) is \(2\), second box is \(18\), third box is \(- 81\)).