Question

Simplify: $({a^2} + 5)({b^3} + 3) + 5$
$A){a^2}{b^3} - 3{a^2} + 5{b^3} + 20$
$B){a^2}{b^3} + 3{a^2} + {b^3} - 20$
$C){a^2}{b^3} + 3{a^2} + 5{b^3} + 20$
$D){a^2}{b^2} + 3{a^2} + 5{b^3} + 20$

Answer 1

Hint: The mathematical operation which we are going to use to solve the problem is multiplication and addition. To expand $({a^2} + 5)({b^3} + 3) + 5$ , we know the multiplication operation $(a + b)(c + d) = a(c + d) + b(c + d)$ . And also we know that $a(c + d) + b(c + d) = ac + ad + bc + bd$ , expand using this and substitute in the given problem.

Complete answer:
Since from given that $({a^2} + 5)({b^3} + 3) + 5$
Starting with the multiplication operation: like $(a + b)(c + d) = a(c + d) + b(c + d)$
Using this method of variable multiplication in the above given problem we get $({a^2} + 5)({b^3} + 3) = {a^2}({b^3} + 3) + 5({b^3} + 3)$
Again, we know that $ \Rightarrow (a + b)(c + d) = a(c + d) + b(c + d) \Rightarrow ac + ad + bc + bd$
Using this method, we get $ \Rightarrow ({a^2} + 5)({b^2} + 3) = {a^2}({b^3} + 3) + 5({b^3} + 3) \Rightarrow {a^2}{b^3} + 3{a^2} + 5{b^3} + 15$
Hence substituting this value in the given problem, we get $({a^2} + 5)({b^3} + 3) + 5 = {a^2}{b^3} + 3{a^2} + 5{b^3} + 15 + 5$
Thus, using the simple addition, we get $15 + 5 = 20$
Hence, we have $({a^2} + 5)({b^3} + 3) + 5 = {a^2}{b^3} + 3{a^2} + 5{b^3} + 20$

Therefore the option C) ${a^2}{b^3} + 3{a^2} + 5{b^3} + 20$ is correct

Note:
Be careful with the power terms, because option C) ${a^2}{b^3} + 3{a^2} + 5{b^3} + 20$, D) ${a^2}{b^2} + 3{a^2} + 5{b^3} + 20$ are more similar and the only difference is ${b^2}$ in the option D.
The other three operations are addition, subtracting, and division.
Subtraction operation, which is the minus of given two or more than two numbers, but here comes with the condition that in subtraction the greater number sign represented in the number will stay constant example $2 - 3 = - 1$
The addition is the sum of given two or more than two numbers, or variables and in addition, if we sum the two or more numbers then we obtain a new frame of the number will be found like $3 + 4 = 7$
The process of the inverse of the multiplication method is called division. Like $x \times y = z$ is multiplication thus the division sees as $x = \dfrac{z}{y}$. Like $\dfrac{4}{2} = 2$ .