Each term in the expression represents part of a side in the area model.
B
b
Note that a^2=a* a.
A
a
8x^2-10x-3
B
b
16x^2-64x+64
Practice makes perfect
a
Each term in the given expression represents a part of a side in the area model. With this information we can draw the following diagram.
Let's calculate the products.
By adding the areas of the smaller rectangles we get the area of the model. This is the same as the product of its sides.
(2x-3)(4x+1)=8x^2+2x-12x-3
⇓
(2x-3)(4x+1)=8x^2-10x-3
To verify Casey's pattern we will multiply the expressions across the diagonals of the rectangle.
If the product of the numbers across one diagonal equals the product of the numbers across the other diagonal, the pattern is correct.
Squaring a number or expression is the same as multiplying it by itself. We can rewrite our expression into multiplication.
(4x-8)^2=(4x-8)(4x-8)
Now we can create our area model.
Let's calculate the products.
By adding the areas of the smaller rectangles we get the area of the model. This is the same as the product of its sides.
(4x-8)^2=16x^2+(- 32x)+(- 32x)+64
⇓
(4x-8)^2=16x^2-64x+64
To verify Casey's pattern we will multiply the expressions across the diagonals of the rectangle.
If the product of the numbers across one diagonal equals the product of the numbers across the other diagonal, the pattern is correct.
