Expand and simplify: (6t 9)(7 5t) – – Solutions Method 1 Use a rectangle diagram. Write (6t 9)(7 5t) as [6t + (–9)][7 + (–5t)] – – Draw a rectangle with dimensions 6t + (–9) and 7 + (–5t). Divide the rectangle into 4 smaller rectangles and label each one. (6t 9)(7 5t) = 42t 30t2 63 + 45t – – – – = + 42t + 45t 63 –30t2 – = + 87t 63 –30t2 – Method 2 Use the distributive property. (6t 9)(7 5t) = (6t)(7 5t) + (–9)(7 5t) – – – – = 42t 30t2 63 + 45t – – = 87t 30t2 63 – – = + 87t 63 –30t2 –
Expand and simplify: (6t – 9)(7 – 5t) Solutions Method 1 Use a rectangle diagram. Write (6t – 9)(7 – 5t) as [6t + (–9)][7 + (–5t)] Draw a rectangle with dimensions 6t + (–9) and 7 + (–5t). Divide the rectangle into 4 smaller rectangles and label each one. (6t – 9)(7 – 5t) = 42t – 30t2 – 63 + 45t = –30t2 + 42t + 45t – 63 = –30t2 + 87t – 63 Method 2 Use the distributive property. (6t – 9)(7 – 5t) = (6t)(7 – 5t) + (–9)(7 – 5t) = 42t – 30t2 – 63 + 45t = 87t – 30t2 – 63 = –30t2 + 87t – 63