(a - 3)^6 5. (r + 2s)^7 6. (4x + y)^4 7. (2 - \frac{m}{2})^5 Find the indicated term of each expansion. 8....

Question

4. (a - 3)^6
5. (r + 2s)^7
6. (4x + y)^4
7. (2 - \frac{m}{2})^5
Find the indicated term of each expansion.
8. third term of (3x - y)^5
9. fifth term of (a + 1)^7
10. fourth term of (j + 2k)^8
11. sixth term of (10 - 3t)^7
12. second term of (m + \frac{2}{3})^9
13. seventh term of (5x - 2)^{11}

SnapAndSolve AI · Accepted Answer

Using the Binomial Theorem, the expansion of (a - 3)^6 is:

(a - 3)^6 = a^6 - 18a^5 + 135a^4 - 540a^3 + 1215a^2 - 1458a + 729
Using the Binomial Theorem, the expansion of (r + 2s)^7 is:

(r + 2s)^7 = r^7 + 14r^6s + 84r^5s^2 + 280r^4s^3 + 560r^3s^4 + 672r^2s^5 + 448rs^6 + 128s^7
Using the Binomial Theorem, the expansion of (4x + y)^4 is:

(4x + y)^4 = 256x^4 + 256x^3y + 96x^2y^2 + 16xy^3 + y^4
Using the Binomial Theorem, the expansion of (2 - \frac{m}{2})^5 is:

(2 - \frac{m}{2})^5 = 32 - 40m + 20m^2 - \frac{20}{4}m^3 + \frac{5}{8}m^4 - \frac{1}{32}m^5
The third term of (3x - y)^5 is:

\binom{5}{2}(3x)^3(-y)^2 = 10 \times 27x^3 \times y^2 = 270x^3y^2
The fifth term of (a + 1)^7 is:

\binom{7}{4}a^3 \times 1^4 = 35a^3
The fourth term of (j + 2k)^8 is:

\binom{8}{3}j^5(2k)^3 = 56j^5 \times 8k^3 = 448j^5k^3
The sixth term of (10 - 3t)^7 is:

\binom{7}{5}(10)^2(-3t)^5 = 21 \times 100 \times (-243t^5) = -5103000t^5
The second term of (m + \frac{2}{3})^9 is:

\binom{9}{1}m^8 \times \left(\frac{2}{3}\right)^1 = 9m^8 \times \frac{2}{3} = 6m^8
The seventh term of (5x - 2)^{11} is:

\binom{11}{6}(5x)^5(-2)^6 = 462 \times 3125x^5 \times 64 = 922560000x^5

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(a - 3)^6 5. (r + 2s)^7 6. (4x + y)^4 7. (2 - \frac{m}{2})^5 Find the indicated term of each expansion. 8....

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