Answer
Verified
377.7k+ views
Hint: For solving these problems, we need to have a clear understanding of the rules of multiplication and indices. By employing the distributive law, and the rules of multiplication of indices, we can easily get the expression for the above problem.
Complete step-by-step solution:
In Maths, Algebra is one of the important branches. The concept of algebra is used to find the unknown variables or unknown quantity. The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants. Algebraic expression is an expression that is built by the combination of integer constants and variables. For example, \[4xy+9\] , in this expression x and y are variables whereas $4$ and $9$ are constants. The value of an algebraic expression changes according to the value chosen for the variables of the expressions.
When a number (let a) is multiplied by itself “n” times. For example, ${{a}^{n}}$ , here, ‘a’ is called the base and ‘n’ is known as the index of the power. Basically, it is an exponential expression. One of the basic rules of the multiplication of indices is ${{a}^{m}}\times {{a}^{n}}={{a}^{mn}}$ .
Distributive property of multiplication over the addition of algebraic expression is:
\[x\times \left( y+z \right)=\left( x\times y \right)+\left( x\times z \right)\]
Employing these laws, we may now write down the given expression as,
\[\begin{align}
& \Rightarrow 3ab\times \left( 5{{a}^{2}}+4{{b}^{2}} \right) \\
& \Rightarrow \left( 3ab\times 5{{a}^{2}} \right)+\left( 3ab\times 4{{b}^{2}} \right) \\
\end{align}\]
Now as we know, ${{a}^{m}}\times {{a}^{n}}={{a}^{mn}}$ , therefore, the expression results in
\[\Rightarrow 15{{a}^{3}}b+12a{{b}^{3}}\]
Thus, multiplication of \[3ab\times \left( 5{{a}^{2}}+4{{b}^{2}} \right)\] gives \[15{{a}^{3}}b+12a{{b}^{3}}\] .
Note: These types of problems are pretty easy to solve, but one needs to be careful otherwise small misjudgements can lead to a totally different answer. We need to carefully employ the properties of multiplication of indices to get to the correct answer and not get confused between the properties as well.
Complete step-by-step solution:
In Maths, Algebra is one of the important branches. The concept of algebra is used to find the unknown variables or unknown quantity. The multiplication of algebraic expressions is a method of multiplying two given expressions consisting of variables and constants. Algebraic expression is an expression that is built by the combination of integer constants and variables. For example, \[4xy+9\] , in this expression x and y are variables whereas $4$ and $9$ are constants. The value of an algebraic expression changes according to the value chosen for the variables of the expressions.
When a number (let a) is multiplied by itself “n” times. For example, ${{a}^{n}}$ , here, ‘a’ is called the base and ‘n’ is known as the index of the power. Basically, it is an exponential expression. One of the basic rules of the multiplication of indices is ${{a}^{m}}\times {{a}^{n}}={{a}^{mn}}$ .
Distributive property of multiplication over the addition of algebraic expression is:
\[x\times \left( y+z \right)=\left( x\times y \right)+\left( x\times z \right)\]
Employing these laws, we may now write down the given expression as,
\[\begin{align}
& \Rightarrow 3ab\times \left( 5{{a}^{2}}+4{{b}^{2}} \right) \\
& \Rightarrow \left( 3ab\times 5{{a}^{2}} \right)+\left( 3ab\times 4{{b}^{2}} \right) \\
\end{align}\]
Now as we know, ${{a}^{m}}\times {{a}^{n}}={{a}^{mn}}$ , therefore, the expression results in
\[\Rightarrow 15{{a}^{3}}b+12a{{b}^{3}}\]
Thus, multiplication of \[3ab\times \left( 5{{a}^{2}}+4{{b}^{2}} \right)\] gives \[15{{a}^{3}}b+12a{{b}^{3}}\] .
Note: These types of problems are pretty easy to solve, but one needs to be careful otherwise small misjudgements can lead to a totally different answer. We need to carefully employ the properties of multiplication of indices to get to the correct answer and not get confused between the properties as well.
Recently Updated Pages
How many sigma and pi bonds are present in HCequiv class 11 chemistry CBSE
Mark and label the given geoinformation on the outline class 11 social science CBSE
When people say No pun intended what does that mea class 8 english CBSE
Name the states which share their boundary with Indias class 9 social science CBSE
Give an account of the Northern Plains of India class 9 social science CBSE
Change the following sentences into negative and interrogative class 10 english CBSE
Trending doubts
Fill the blanks with the suitable prepositions 1 The class 9 english CBSE
The Equation xxx + 2 is Satisfied when x is Equal to Class 10 Maths
In Indian rupees 1 trillion is equal to how many c class 8 maths CBSE
Which are the Top 10 Largest Countries of the World?
How do you graph the function fx 4x class 9 maths CBSE
Give 10 examples for herbs , shrubs , climbers , creepers
Difference Between Plant Cell and Animal Cell
Difference between Prokaryotic cell and Eukaryotic class 11 biology CBSE
Why is there a time difference of about 5 hours between class 10 social science CBSE