Answer:
1. 12a⁹b⁷
2. 6s⁹t⁶
3. y³ + 3y² + 3y +1
Step-by-step explanation:
1. 4a³b² × 3a⁶b⁵
i) multiply the numbers
= (4×3)a³b² × a⁶b⁵
= 12a³b²a⁶b⁵
ii) rearrange the terms
= 12a³a⁶b²b⁵
iii) multiply the terms with the same base by adding their exponents
[tex] = 12 {a}^{3+ 6} {b}^{2 + 5} [/tex]
iv) add the numbers
= 12a⁹b⁷
2. 6s⁵t × s⁴t²
i) rearrange the terms
= 6s⁵s⁴tt²
ii) multiply the terms with the same base by adding their exponents
[tex] = {6s}^{5 + 4} {t}^{1 + 2} [/tex]
iii) add the numbers
= 6s⁹t⁶
[tex]3. \frac{(y + 1) {}^{5} }{(y + 1) {}^{2} } [/tex]
i) simplify the expression by substracting the exponents
[tex] = {(y + 1)}^{5 - 2} [/tex]
[tex] = (y + 1) {}^{3} [/tex]
ii) expand the expression using the formula below:
(a+b)³ = a³ + 3a²b + 3ab² + b³
[tex] = {y}^{3} + 3 {y}^{3} + 3y + 1[/tex]
