Question

find the product (5 - 2x - x^2) (3 - 2x)​

Answer 1

Given:

• (5 - 2x - x²) (3 - 2x)

To find:

• Find the product ?

Solution:

• Let two factors of the expression be (5 - 2x - x²) & (3 - 2x).

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• Let (3 - 2x) divided into two terms, They will be multiplied with (5 - 2x - x²)

They are,

• 3
• -2x

(5 - 2x - x²) (3 - 2x)

→ 3(5 - 2x - x²) - 2x(5 - 2x - x²)

→ 15 - 6x - 3x² - 10x + 4x² + 2x³

→ 15 - 6x - 10x + 4x² - 3x² + 2x³

→ 15 - 16x + 4x² - 3x² + 2x³

→ 15 - 16x + 1x² + 2x³

∴ Hence, Product of (5 - 2x - x²) (3 - 2x) is 15 - 16x + 1x² + 2x³.

Additional Information:

• (a + b)² = a² + 2ab + b²

• (a - b)² = a² - 2ab + b²

• a² + b² = (a + b)² - 2ab

• a² + b² = (a - b)² + 2ab

• (a + b)³ = a³ + 3a²b + 3ab² b³

• (a + b)³ = a³ + b³ + 3ab(a + b)

• (a - b)³ = a³ - 3a²b + 3ab² - b³

• a³ + b³ = (a + b)( a² - ab + b² )

• a³ + b³ = (a + b)³ - 3ab( a + b)

• a³ - b³ = (a - b)( a² + ab + b²)

• a³ - b³ = (a - b)³ + 3ab ( a - b )

Answer 2

Given : $\qquad \sf (5 - 2x - x^2) (3 - 2x)$

Exigency to find : The Product of : $\qquad \sf (5 - 2x - x^2) (3 - 2x)$

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$\qquad \dag\:\:\bigg\lgroup \sf{ (5 - 2x - x^2) (3 - 2x) }\bigg\rgroup$

⠀⠀⠀⠀⠀Finding the product of : ( 5 - 2x - x² ) ( 3 - 2x )

$\qquad \longmapsto \sf (5 - 2x - x^2) (3 - 2x)$

$\qquad \longmapsto \sf 3 (5 - 2x - x^2) - 2x (5 - 2x - x^2)$

$\qquad \longmapsto \sf 15 - 6x - 3x^2 - 10x + 4x^2 + x^3$

$\qquad \longmapsto \sf 15 - 6x -10x + 4x^2 - 3x^2 + x^3$

$\qquad \longmapsto \bf \bigg( 15 - 16x + x^2 + x^3 \bigg)\:\qquad \longrightarrow \:\: Required \:AnswEr \:$

Therefore,

⠀⠀⠀⠀⠀$\therefore {\underline{ \mathrm {\:Hence, \:The\:Product \:is\:\bf{15 - 16x + x^2 + x^3 }}}}$

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$\large {\boxed{\sf{\mid{\overline {\underline {\star More\:To\:know\::}}}\mid}}}$

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

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