Question

(2x-5y) (2x-5y)solve by identities​

Answer 1

Given Equation:-

$\\ \sf{\bold{(2x - 5y)(2x - 5y)}}$

To Do:-

$\\\sf{\rightarrow{Solve \: by \: identities }}$

Formula Applied:-

$\\\sf{\bold{(a - b) {}^{2} } = {a}^{2} - 2ab + {b}^{2} }$

Solution:-

$\\\sf{\bold{(2x - 5y)(2x - 5y)}}$

$\\\sf{\implies{(2x - 5y) {}^{2} }}$

$\\ \sf{Comparing \: this \: equation \: with \: {(a - b)}^{2} , \: we \: find,}$

$\sf{\bold{a} = 2x\: and \: \bold{b} = \sf{5y}}$

Now, applying the formula;-

$\\ \sf{ {(2x)}^{2} - 2 \times 2x \times 5y + {(5y)}^{2}}$

$\\ \sf{\therefore{\red{4 {x}^{2} - 20xy + 25 {y}^{2} }}}$

$\\\underline{\boxed{\rm{Hence, \: the \: answer \: is \: \bold{4 {x}^{2} - 20xy + 25 {y}^{2} }}}}$

More Important Formulas:-

$\\\sf{\bold{(a + b) {}^{2}} = {a}^{2} + 2ab + {b}^{2} } \\ \\ \sf{\bold{(a - b) {}^{2}} = {a}^{2} - 2ab + {b}^{2} }$

$\\ \sf{\bold{(a - b) {}^{3}} = {a}^{3} - 3 {a}^{2}b + 3a {b}^{2} - {b}^{3} } \\ \\\sf{\bold{(a + b) {}^{3}} = {a}^{3} + 3 {a}^{2}b + 3a {b}^{2} + {b}^{3} }$

Answer 2

$\huge\bold\red{Answer:-}$

(2x-5y) (2x-5y)

$\implies(2x-5y^2)$

Applying the Formula :-

$a-b^2=a^2+2ab+b^2$

= $(2x^2)-2×2x×5y+(5y^2)$

=$4x^2-20xy+25y^2$