Question

Factorise the following, using the identity a² + 2ab + b² = (a+b)²

(i). a²x² + 2ax + 1 (ii). 9x² + 30x + 25​

Answer 1

Given:-

We have to solve these using identity $a^{2} + 2ab + b^{2} = ( a + b )^{2}$.

Solution:-

(i)   $a^{2}x^{2} + 2ax + 1$

⇒ $( ax )^{2}$ + $2$ × $a$$x$ × $1$ + $1^{2}$

⇒ $( ax + 1 )^{2}$

(ii)   $9x^{2} + 30x + 25$

⇒ $( 3x )^{2}$ + $2$ × $3x$ × $5$ + $5^{2}$

⇒ $( 3x + 5 )^{2}$

         $\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebric\:Identity}}\:\bigstar}\\\\1)\bf\:(A+B)^{2} = A^{2} + 2AB + B^{2}\\\\2)\sf\: (A-B)^{2} = A^{2} - 2AB + B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\sf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\sf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) + B^{3}\\\\8)\sf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\\end{minipage}}$

Some Important tips:-

• To Factorize any expression firstly check it have any common terms or constant common terms and then factorize.

For Example :- $8x^{2} + 4x + 2$

                   ⇒ $2 ( 4x^{2} + 2x + 1 )$

                   ⇒ $2 [ (2x)^{2}$ + $2$ × $2x$ × $1$ + $1^{2} ]$

                   ⇒ $2 [( 2x + 1 )^{2}]$

Answer 2

Answer:

hey answer is here

Step-by-step explanation:

(ax) ²+2×ax×1+1²

(ax+1)²

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