Question

expand the polynomial
${(2+ 3)}^{2} \\ {(2 - 3)}^{2}$
​

Answer 1

Answer:

${2}^{2} + 2 \times 3 + {3}^{2}$

$= > 4 + 2(6) + 9$

$= > 4 + 12 + 9$

$= > 25$

${2}^{2} - 2(2)(2) + {3}^{2}$

$= > 4 - 2(6) + 9$

$13 - 9$

$= > 4$

Answer 2

Question:

Expand the following:-

⊙(2+3)²

⊙(2-3)²

Answer:

⊙(2+3)²

$\sf : \implies2²+3²+2(2)(3)$

$\sf : \implies4+9+12$

$\sf : \implies25$

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⊙(2-3)²

$\sf : \implies 2²+3²-2(2)(3)$

$\sf : \implies 4+9-12$

$\sf :\implies 1$

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Algebric Identities :

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