Question

for problems 13 - 17, find the product. write your answer in standard form. 13. (m + 2)(m + 5) 14. (a - 1)(a + 6) 15. (9 - v)(v - 3) 16. (7z - 2)(3z + 2) 17. (n + 2/3)(n + 5/3) 18. write a polynomial expression in standard form for the area of a rectangle with length d + 6 and width d + 9, where d > -6.

Explanation:

Step1: Use FOIL method for (m + 2)(m + 5)

$(m + 2)(m + 5)=m\times m+m\times5+2\times m + 2\times5=m^{2}+5m+2m + 10$

Step2: Combine like - terms

$m^{2}+(5m+2m)+10=m^{2}+7m + 10$

Step3: Use FOIL method for (a - 1)(a + 6)

$(a - 1)(a + 6)=a\times a+a\times6+(-1)\times a+(-1)\times6=a^{2}+6a - a-6$

Step4: Combine like - terms

$a^{2}+(6a - a)-6=a^{2}+5a - 6$

Step5: Use FOIL method for (9 - v)(v - 3)

$(9 - v)(v - 3)=9\times v+9\times(-3)+(-v)\times v+(-v)\times(-3)=9v-27 - v^{2}+3v$

Step6: Combine like - terms

$-v^{2}+(9v + 3v)-27=-v^{2}+12v - 27$

Step7: Use FOIL method for (7z - 2)(3z + 2)

$(7z - 2)(3z + 2)=7z\times3z+7z\times2+(-2)\times3z+(-2)\times2=21z^{2}+14z-6z - 4$

Step8: Combine like - terms

$21z^{2}+(14z - 6z)-4=21z^{2}+8z - 4$

Step9: Use FOIL method for $(n+\frac{2}{3})(n+\frac{5}{3})$

$(n+\frac{2}{3})(n+\frac{5}{3})=n\times n+n\times\frac{5}{3}+\frac{2}{3}\times n+\frac{2}{3}\times\frac{5}{3}=n^{2}+\frac{5}{3}n+\frac{2}{3}n+\frac{10}{9}$

Step10: Combine like - terms

$n^{2}+(\frac{5}{3}n+\frac{2}{3}n)+\frac{10}{9}=n^{2}+\frac{7}{3}n+\frac{10}{9}$

Step11: Use FOIL method for rectangle area with length d + 6 and width d + 9

$(d + 6)(d + 9)=d\times d+d\times9+6\times d+6\times9=d^{2}+9d+6d + 54$

Step12: Combine like - terms

$d^{2}+(9d+6d)+54=d^{2}+15d + 54$

Answer:

1. $m^{2}+7m + 10$
2. $a^{2}+5a - 6$
3. $-v^{2}+12v - 27$
4. $21z^{2}+8z - 4$
5. $n^{2}+\frac{7}{3}n+\frac{10}{9}$
6. $d^{2}+15d + 54$