Question

How do you simplify \[3a \times 4a\]?

Answer 1

Hint: The algebraic expression should be any one of the forms such as addition, subtraction, multiplication and division. Hence, here we need to perform multiplication i.e., the given expression consists of two terms, in which we need to multiply both the terms as directed. As there is a constant variable ‘a’ involved and to solve this expression, combine the exponents terms and then simplify to get the product.

Complete step by step answer:
Given,
\[3a \times 4a\],
which is 3a times 4a i.e.,
\[3a \cdot 4a\]
Hence, to simplify the given expression we need to multiply the terms to get the product,
\[3 \cdot 4 \cdot a \cdot a\]
\[ \Rightarrow 12a \cdot a\]
Hence, combining the exponents we get:
\[ \Rightarrow 12{a^2}\]

Therefore,
\[3a \times 4a = 12{a^2}\]

Additional information:
Use exponent rules to remove parentheses in terms with exponents and also to remove grouping if the terms are containing exponents and combine the like terms by addition or subtraction and if the expression consists of constants then, combine the constants and simplify the expression. If the expression consists of large exponents then to solve this, requires factoring. If you factor the exponent down until all the factors are prime numbers you can then apply the power rule of exponents to solve the expression.

Note: The key point to solve the given expression we must know all the arithmetic functions, such that to solve any expression of these kind simplification is possible if and only if we know how to perform the arithmetic functions with respect to its exponents. Hence, based on the given expression we must simplify the given terms.