Homework SourseMultiplying Special Case Polynomials 1 Find each product A 7
Multiplying Special Case Polynomials
1. Find each product
A. (7u+4v)(7u-4v)
B. (-y-3x)(-y+3x)
C. (-9x2 -10y)2
Please no handwritten work. Thank You.
Solution
1.(7u+4v) (7u-4v)
Using identity (a+b) (a-b) = a2 - b2, here a=7u and b=4v
(7u+4v) (7u-4v) = (7u)2 - (4v)2 = 49u2 - 16v2
2.(-y-3x) (-y+3x)
Using same identity as in above where a=-y and b=3x
(-y-3x) (-y+3x) = (-y)2 - (3x)2 = y2 - 9x2
3. (-9x2 - 10y)2
Using identity (a-b)2 = a2 - 2ab + b2, where a=-9x and b=10y
(-9x2 - 10y)2 = (-9x)2 - 2(-9x)(10y) + (10y)2 = 81x2 + 180xy + 100y2
4. (4u + 9v)2
Using identity (a+b) = a2 + 2ab + b2, where a=4u and b=9v
(4u + 9v)2 = (4u)2 + 2(4u)(9v) + (9v)2 = 16u2 + 72uv + 81v2
5. (7u+6v) (7u-6v)
Using identity used in Question 1. , where a=7u and b=6v
(7u+6v) (7u-6v) = (7u)2 - (6v)2 = 49u2 - 36v2
6. (-6x - 7y2)2 = -(6x + 7y2)2
Using identity used in Question 4. , where a=6x and b=7y
-(6x + 7y2)2 = -[(6x)2 + 2(6x)(7y2) + (7y2)2] = -[362 + 84xy2 + 49y4] = -362 - 84xy2 - 49y4
