IM Alg1.6.8 Lesson: Equivalent Quadratic Expressions
Explain why the diagram shows that .
Draw a diagram to show that 5(x+2)=5x+10.
Applying the distributive property to multiply out the factors of, or expand, gives us , so we know the two expressions are equivalent. We can use a rectangle with side lengths and 4 to illustrate the multiplication.
Draw a diagram to show that n(2n+5) and 2n²+5n are equivalent expressions.
For each expression, use the distributive property to write an equivalent expression. If you get stuck, consider drawing a diagram.
Here is a diagram of a rectangle with side lengths x+1 and x+3.
Use this diagram to show that and are equivalent expressions.
Draw diagrams to help you write an equivalent expression for each of the following: (x+5)²
Draw diagrams to help you write an equivalent expression for each of the following: 2x(x+4)
Draw diagrams to help you write an equivalent expression for each of the following: (2x+1)(x+3)
Draw diagrams to help you write an equivalent expression for each of the following: (x+m)(x+n)
Write an equivalent expression for each expression without drawing a diagram:
Is it possible to arrange an by square, five by 1 rectangles and six 1 by 1 squares into a single large rectangle? Explain or show your reasoning.
What does this tell you about an equivalent expression for ?
Is there a different non-zero number of 1 by 1 squares that we could have used instead that would allow us to arrange the combined figures into a single large rectangle?