Question

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Answer 1

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

$= 12 {a}^{3+ 6} {b}^{2 + 5}$

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

$= {6s}^{5 + 4} {t}^{1 + 2}$

iii) add the numbers

= 6s⁹t⁶

$3. \frac{(y + 1) {}^{5} }{(y + 1) {}^{2} }$

i) simplify the expression by substracting the exponents

$= {(y + 1)}^{5 - 2}$

$= (y + 1) {}^{3}$

ii) expand the expression using the formula below:

(a+b)³ = a³ + 3a²b + 3ab² + b³

$= {y}^{3} + 3 {y}^{3} + 3y + 1$