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 + 24x 2 - 6y 2 - 154x 2 + 8xy - 12x - 3y + 54x 2 - 6y 2 + 5xy - 7x + 19y - 15

Answer:See explanationStep-by-step explanation:1.[tex](a+b)(a^2-ab+b^2)=a^3-a^2b+ab^2+a^2b-ab^2+b^3=a^3+b^3[/tex]2.[tex](1-7x)(1+9x)=1+9x-7x-63x^2=-63x^2+2x+1[/tex]3.[tex](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[/tex]4.[tex](a-b)(a^2+ab+b^2)=a^3+a^2b+ab^2-a^2b-ab^2-b^3=a^3-b^3[/tex]5.[tex](m^3n+8)(m^3n-5)=(m^3n)^2-5m^3n+8m^3n-40=m^6n^2+3m^3n-40[/tex]6. [tex](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[/tex]7. [tex](ab-9)(ab+8)=(ab)^2+8ab-9ab-72=a^2b^2-ab-72[/tex]8. [tex](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[/tex]9. [tex](a+3)(a-2)=a^2-2a+3a-6=a^2+a-6[/tex]10.[tex](3m^3-y)(3m^3-y)=(3m^3)^2-3m^3y-3m^3y+y^2=9m^6-6m^3y+y^2[/tex]11.[tex](2x-3y)(4x-y)=8x^2-2xy-12xy+3y^2=8x^2-14xy+3y^2[/tex]12.[tex](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[/tex]13.[tex](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[/tex]