Question

Simplify the following expressions: (2x+7y) (x-3y) – (9x+4) (3x-2) proper solution​

Answer 1

Question:

Simplify the following expressions:

$(2x + 7y)(x - 3y) - (9x + 4)(3x - 2)$

To find:

★ To find simplify the given expression.

Answer:

$The \: value \: is \: \underline{ \:\underline{ \: \sf \pink{25 {x}^{2} - xy - 6x + 21 {y}^{2} - 8} \: }\: }$

Given:

★ An expression is given,

$\sf{(2x + 7y)(x - 3y) - (9x + 4)(3x - 2)}$

Step-by-step explanation:

$(2x + 7y)(x - 3y) - (9x + 4)(3x - 2)$

$= 2 {x}^{2} - 6xy + 7xy - 21 {y}^{2} - \big[27 {x}^{2} - 18x + 12x - 8 \big]$

$= 2 {x}^{2} + xy - 21 {y}^{2} - 27 {x}^{2} + 18x - 12x + 8$

$= - 25 {x}^{2} + xy + 6x - 21 {y}^{2} + 8$

$It \: also \: can \: be \: written \: as,$

$\implies \boxed{25 {x}^{2} - xy - 6x + 21 {y}^{2} - 8}$

$\therefore The \: value \: is \: \underline{ \:\underline{ \: \bold{25 {x}^{2} - xy - 6x + 21 {y}^{2} - 8} \: }\: }$

Formulae to know:

$\bigstar {(a + b)}^{2} = {a}^{2} + 2ab + {b}^{2}$

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

$\bigstar {a}^{2} - {b}^{2} = (a - b)(a + b)$

$\bigstar {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2} )$

$\bigstar {a}^{3} - {b}^{3} = (a - b)( {a}^{2} + ab + {b}^{2} )$