Multiply polynomials vertically and horizontally

1
EXAMPLE 3
Multiply polynomials vertically and horizontally
SOLUTION
Multiply 2y2 3y 6 by 2 .
2y3 3y2 6y
Multiply 2y2 3y 6 by y
Combine like terms.
2
EXAMPLE 3
Multiply polynomials vertically and horizontally
b. (x 3)(3x2 2x 4) (x 3)3x2 (x
3)2x (x 3)4
3x3 9x2 2x2 6x 4x 12
3x3 7x2 2x 12
3
EXAMPLE 4
Multiply three binomials
Multiply x 5, x 1, and x 3 in a horizontal
format.
(x 5)(x 1)(x 3) (x2 4x 5)(x 3)
(x2 4x 5)x (x2 4x 5)3
x3 4x2 5x 3x2 12x 15
x3 x2 17x 15
4
EXAMPLE 5
Use special product patterns
a. (3t 4)(3t 4)
Sum and difference
(3t)2 42
9t2 16
b. (8x 3)2
(8x)2 2(8x)(3) 32
Square of a binomial
64x2 48x 9
Cube of abinomial
c. (pq 5)3
(pq)3 3(pq)2(5) 3(pq)(5)2 53
p3q3 15p2q2 75pq 125
5
for Examples 3, 4 and 5
GUIDED PRACTICE
Find the product.
3. (x 2)(3x2 x 5)
3x3 5x2 7x 10
ANSWER
4. (a 5)(a 2)(a 6)
(a3 3a2 28a 60)
ANSWER
5. (xy 4)3
x3y3 12x2y2 48xy 64
ANSWER