8­4 Multiplying Special Cases binomial ​
(noun) by n o h mee ul Related Words:​
square of a binomial Definition:​
A binomial is a polynomial with two terms. Essential Understanding​
There are special rules you can use to simplify the square of a binomial or the product of a sum and difference. 2
2
Squares of binomials have the form (a + b) or (a − b) . You can algebraically simplify the product or you can use an area model to discover the rule for 2
simplifying (a + b) , as shown below. Simplify each expression. 2
A.) (w + 5) 2
B.) (3s + 9) 2
C.) (a − 8) 2
D.) (5m − 2) E.) ​
Geometry​
The figures below are squares. Find an expression for the area of each shaded region. Write your answers in standard form. F.) ​
Interior Design​
A square green rug has a Blue square in the center. The side length of the blue square is x inches. The width of the green band that surrounds the blue square is 6 in. What is the area of the green band? Using Mental math, you can square a binomial to find the square of a number. Simplify each product. G.) 792 H.) 4032 The product of the sum and the difference of the same two terms also produces a pattern. Simplify each product. I.) (v + 6) (v − 6)
J.) (z − 5) (z + 5) K.) (10 + y) (10 − y) You can use the rule for the product of a sum and difference to calculate products using mental math. Simplify each product. L.) 42 • 38
M.) 63 • 57 N.) 303 • 297
2
O.) (2a + b) 2
P.) (g − 7h) 2
Q.) (8r − 5s) (
R.) p4 − 9q2
2
) S.) (a − 6b) (a + 6b) T.) (r2 + 3s) (r2 − 3s) (
U.) 3w3 − z2
) (3w
3
)
+ z2