Question

(iv) a power4+6asquareb square +9 b power 4
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Answer 1

ANSWER:

To Simplify:

• $a^4+6a^2b^2+9b^4$

Solution:

We are given that,

$\implies a^4+6a^2b^2+9b^4$

We can rewrite it as,

$\implies (a^2)^2+6a^2b^2+(3b^2)^2$

$\implies (a^2)^2+2(a^2)(3b^2)+(3b^2)^2$

We know that,

$\hookrightarrow x^2+2xy+y^2=(x+y)^2$

On comparing the formula with the obtained expression,

$\implies x=a^2\:\&\:y=3b^2$

So,

$\implies (a^2)^2+2(a^2)(3b^2)+(3b^2)^2$

$\implies (a^2+3b^2)^2$

Hence,

$\implies\bf a^4+6a^2b^2+9b^4= (a^2+3b^2)^2$

Formula Used:

• $x^2+2xy+y^2=(x+y)^2$

Learn More:

$\boxed{\begin{minipage}{7 cm}\boxed{\bigstar\:\:\textbf{\textsf{Algebraic\:Identities}}\:\bigstar}\\\\1)\bf\: (A+B)^{2} =A^{2}+2AB+B^{2}\\\\2)\bf\: (A-B)^{2}=A^{2}-2AB+B^{2}\\\\3)\bf\: A^{2} - B^{2} = (A+B)(A-B)\\\\4)\bf\: (A+B)^{2} = (A-B)^{2} + 4AB\\\\5)\bf\: (A-B)^{2} = (A+B)^{2} - 4AB\\\\6)\bf\: (A+B)^{3} = A^{3} + 3AB(A+B) + B^{3}\\\\7)\bf\:(A-B)^{3} = A^{3} - 3AB(A-B) - B^{3}\\\\8)\bf\: A^{3} + B^{3} = (A+B)(A^{2} - AB + B^{2})\\\\9)\bf\: A^{3} - B^{3} = (A-B)(A^{2} + AB + B^{2})\\\\ \end{minipage}}$

Answer 2

Answer:

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