Question

factorise using identities
plz answer this ​

Answer 1

$\huge{ \underline{\frak{\:\:\:\:\:~~~~~ \bigstar{}Solution\:\:\:\:\:~~~~~}}}$

Equation 1:

$\boxed{ \bf{}(x + {y)}^{2} - (x - {y)}^{2} }$

Now Let's solve it!

$\dashrightarrow \sf{}(x + {y)}^{2} - (x - {y)}^{2}$

$\dashrightarrow \sf{}(x^{2} + {y}^{2} + 2xy) - (x - {y)}^{2}$

$\dashrightarrow \sf{}(x^{2} + {y}^{2} + 2xy) - ( {x}^{2} + {y}^{2} - 2xy)$

$\dashrightarrow \sf{}(x^{2} + {y}^{2} + 2xy) -{x}^{2} - {y}^{2} + 2xy$

$\dashrightarrow \sf{}x^{2} + {y}^{2} + 2xy -{x}^{2} - {y}^{2} + 2xy$

$\dashrightarrow \sf{}x^{2}+ 2xy -{x}^{2} - {y}^{2}+ {y}^{2} + 2xy$

$\dashrightarrow \sf{}x^{2}+ 2xy -{x}^{2}\cancel{ - {y}^{2}}+\cancel{ {y}^{2} }+ 2xy$

$\dashrightarrow \sf{}x^{2}+ 2xy -{x}^{2}+ 2xy$

$\dashrightarrow \sf{}x^{2}-{x}^{2}+ 2xy + 2xy$

$\dashrightarrow \sf{}\cancel{x^{2}}\cancel{-{x}^{2}}+ 2xy + 2xy$

$\dashrightarrow \sf{}2xy + 2xy$

$\dashrightarrow \underline{\boxed{\sf{}4xy}}$

Or:

$\dashrightarrow \sf{}(x + {y)}^{2} - (x - {y)}^{2}$

$\dashrightarrow \sf{}(x + y + x - y)(x + y - x + y)$

$\dashrightarrow \sf{}(x\cancel{ + y }+ x \cancel{- y})(\cancel{x }+ y \cancel{- x} + y)$

$\dashrightarrow \sf{}(x + x)(y + y)$

$\dashrightarrow \sf{}2x \times 2y$

$\dashrightarrow \underline{\boxed{\sf{}4xy}}$

Equation 2:

$\boxed{ \bf{} \bigg( \frac{9}{25} {a}^{2} \bigg) - \bigg( \frac{16}{64} {b}^{2} \bigg) }$

Now Let's solve it!

$\dashrightarrow\sf{} \bigg( \dfrac{9}{25} {a}^{2} \bigg) - \bigg( \dfrac{16}{64} {b}^{2} \bigg)$

$\dashrightarrow\sf{} \bigg( \dfrac{3 \times 3}{5 \times 5} {a}^{2} \bigg) - \bigg( \dfrac{4 \times 4}{8 \times 8} {b}^{2} \bigg)$

$\dashrightarrow\sf{} \bigg( \dfrac{ {3}^{2} }{ {5}^{2} } {a}^{2} \bigg) - \bigg( \dfrac{ {4}^{2} }{ {8}^{2} } {b}^{2} \bigg)$

$\dashrightarrow\sf{} \bigg( \dfrac{ {3}}{ {5} } {a}\bigg)^{2} - \bigg( \dfrac{ {4}}{ {8}} {b} \bigg)^{2}$

$\dashrightarrow \underline{ \boxed{\sf{} \bigg( \dfrac{ {3}}{ {5} } {a} + \dfrac{4}{8}b \bigg) \bigg( \dfrac{3}{5} a - \dfrac{ {4}}{ {8}} {b} \bigg)}}$

know more:

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

@DüllStâr