Simplify the following expressions: 3 (ii): (a2 + 5)(b3 + 3) + 5 and 3 (iii): (t + s2)(t2 - s)

Question

ScanSolve AI Tutor · Accepted Answer

Here are the solutions for questions 3 (ii) and 3 (iii):

3. Simplify.

Multiply the binomials $(a^2 + 5)$ and $(b^3 + 3)$ using the distributive property (FOIL method).
$$ (a^2 + 5)(b^3 + 3) = a^2(b^3) + a^2(3) + 5(b^3) + 5(3) $$ $$ = a^2b^3 + 3a^2 + 5b^3 + 15 $$
Add the constant 5 to the result from Step 1.
$$ a^2b^3 + 3a^2 + 5b^3 + 15 + 5 $$
Combine the constant terms.
$$ = \boxed{a^2b^3 + 3a^2 + 5b^3 + 20} $$
- 3 (iii): $(t + s^2)(t^2 - s)$
Multiply the binomials $(t + s^2)$ and $(t^2 - s)$ using the distributive property (FOIL method).
$$ (t + s^2)(t^2 - s) = t(t^2) + t(-s) + s^2(t^2) + s^2(-s) $$
Perform the multiplications.
$$ = \boxed{t^3 - ts + s^2t^2 - s^3} $$

Step-by-step solution