Question

Place the indicated product in the proper location on the grid.
1. (a + b)(a 2 - ab + b 2)

2. (1 - 7x)(1 + 9x)

3. (x + y + 3)(x + y - 4)

4. (a - b)(a 2 + ab + b 2)

5. (m 3 n + 8)(m 3 n - 5)

6. [4 - (3c - 1)][6 - ( 3c - 1)]

7. (ab - 9)(ab + 8)

8. (a + b - c)(a + b + c)

9. (a + 3)(a - 2)

10. (3m 3 - y)(3m 3 - y)

11. (2x - 3y)(4x - y)

12. Place the indicated product in the proper location on the grid. Write your answer in descending powers of x.
(x 2 + 2x - 1)(x 2 + 2x + 5)

13. Which of the following polynomials corresponds to the product of the multivariate polynomials 4x - 3y + 5 and x + 2y -3?
5x - y + 2
4x 2 - 6y 2 - 15
4x 2 + 8xy - 12x - 3y + 5
4x 2 - 6y 2 + 5xy - 7x + 19y - 15

Answer 1

Answer:

See explanation

Step-by-step explanation:

1.

$(a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3=a^3+b^3$

2.

$(1-7x)(1+9x)=1+9x-7x-63x^2=-63x^2+2x+1$

3.

$(x+y+3)(x+y-4)=x^2+xy-4x+xy+y^2-4y+3x+3y-12=x^2+2xy+y^2-x-y-12$

4.

$(a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3=a^3-b^3$

5.

$(m^3n+8)(m^3n-5)=(m^3n)^2-5m^3n+8m^3n-40=m^6n^2+3m^3n-40$

6.

$(4-(3c-1))(6-(3c-1))=(4-3c+1)(6-3c+1)=(5-3c)(7-3c)=35-15c-21c+9c^2=9c^2-36c+35$

7.

$(ab-9)(ab+8)=(ab)^2+8ab-9ab-72=a^2b^2-ab-72$

8.

$(a+b-c)(a+b+c)=a^2+ab+ac+ab+b^2+bc-ac-bc-c^2=a^2+b^2-c^2+2ab$

9.

$(a+3)(a-2)=a^2-2a+3a-6=a^2+a-6$

10.

$(3m^3-y)(3m^3-y)=(3m^3)^2-3m^3y-3m^3y+y^2=9m^6-6m^3y+y^2$

11.

$(2x-3y)(4x-y)=8x^2-2xy-12xy+3y^2=8x^2-14xy+3y^2$

12.

$(x^2+2x-1)(x^2+2x+5)=x^4+2x^3+5x^2+2x^3+4x^2+10x-x^2-2x-5=x^4+4x^3+8x^2+8x-5$

13.

$(4x-3y+5)(x+2y-3)=4x^2+8xy-12x-3xy-6y^2+9y+5x+10y-15=4x^2+5xy-6y^2-7x+19y-15$