Question

factorise ( a+2b)²-(2a+b)²​

Answer 1

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Answer 2

Given: The equation is$( a+2b)^{2} -(2a+b)^{2}$.

We have to solve the above equation.

By using the Bodmas rule, we are solving the above equation.

As we know that the Bodmas rule is used to remember the order of operations to be followed while solving expressions in mathematics.

Where,

$\begin{array}{l}\mathrm{B}=\text{brackets}\\\mathrm{O}=\text { order of powers or rules } \\\mathrm{D}=\text { division } \\\mathrm{M}=\text { multiplication } \\\mathrm{A}=\text { addition } \\\mathrm{S}=\text { subtraction }\end{array}$

We are solving in the following way:

We have,

$( a+2b)^{2} -(2a+b)^{2}$

We know that$(a+b)^{2} =a^{2} +2ab+b^{2}$

So,

$=>a^{2} +4ab+4b^{2} -(4a^{2} +4ab+b^{2} )\\=>a^{2} +4ab+4b^{2} -4a^{2} -4ab-b^{2} \\=>-3a^{2}+3b^{2}$

Hence, the solution of the given equation will be$-3a^{2}+3b^{2}$.