Answer Key 221Chapter 9 Multiplying Polynomials
Exercise 9
- (4x^5 y^3 )(−3x^2 y^3 ) = −12x^7 y^6
- (−8a^4 b^3 )(5ab^2 ) = −40a^5 b^5
- (−10x^3 )(−2x^2 ) = 20 x^5
- (−3x^2 y^5 )(6xy^4 )(−2xy) = 36 x^4 y^10
- 3(x − 5) = 3x − 15
- x(3x^2 − 4) = 3 x^3 − 4x
- −2a^2 b^3 (3a^2 – 5ab^2 – 10)
= −2a^2 b^3 ⋅ 3 a^2 + 2 a^2 b^3 ⋅ 5ab^2 +
2a^2 b^3 ⋅ 10
= −6a^4 b^3 + 10 a^3 b^5 + 20 a^2 b^3 - (2x − 3)(x + 4)
= 2 x^2 + 8 x − 3x − 12
= 2 x^2 + 5 x − 12 - (x + 4)(x + 5)
= x^2 + 5 x + 4 x + 20
= x^2 + 9 x + 20 - (x − 4)(x − 5)
= x^2 − 5x − 4x + 20
= x^2 − 9x + 20 - (x + 4)(x − 5)
= x^2 − 5x + 4 x − 20
= x^2 − x − 20 - (x − 4)(x + 5)
= x^2 + 5 x − 4x − 20
= x^2 + x − 20 - (x − 1)(2x^2 − 5x + 3)
= 2 x^3 − 5x^2 + 3 x − 2x^2 + 5 x − 3
= 2 x^3 − 7x^2 + 8 x − 3
14. (2x^2 + x − 3)(5x^2 − x − 2)
= 10 x^4 − 2x^3 − 4x^2 + 5 x^3 − x^2 − 2x −
15 x^2 + 3 x + 6
= 10 x^4 + 3 x^3 − 20x^2 + x + 6
15. (x − y)^2
= (x − y)(x − y)
= x^2 − xy − xy + y^2
= x^2 – 2xy + y^2
16. (x + y)(x − y)
= x^2 − xy + xy − y^2
= x^2 − y^2
17. (x + y)^3
= (x + y)(x + y)(x + y)
= (x + y)(x^2 + 2 xy + y^2 )
= x^3 + 2 x^2 y + xy^2 + x^2 y + 2 xy^2 +y^3
= x^3 + 3 x^2 y + 3 xy^2 +y^3
18. (x − y)^3
= (x − y)(x − y)(x − y)
= (x − y)(x^2 – 2xy + y^2 )
= x^3 − 2x^2 y + xy^2 − x^2 y + 2 xy^2 − y^3
= x^3 − 3x^2 y + 3 xy^2 – y^3
19. (x + y)(x^2 – xy + y^2 )
= x^3 − x^2 y + xy^2 + x^2 y − xy^2 + y^3
= x^3 + y^3
20. (x − y)(x^2 + xy + y^2 )
= x^3 + x^2 y + xy^2 − x^2 y − xy^2 − y^3
= x^3 − y^3