Question

evaluate using identites 54^2 - 46^2

Answer 1

Answer:

800

Step-by-step explanation:

(a+b)(a-b)=a^2-b^2

(54+46)(54-46)

100*8

800

Answer 2

Answer :

• 800

Using Formula :

$\small \boxed{ \begin{gathered} \bf (a + b)(a - b) \\ \rm=a(a-b)+b(a-b) \\ \rm=a^2-ab+ba-b^2 \\ \rm=a^2-ab+ab-b^2 \\ \bf=a^2-b^2 \end{gathered}}$

Solution :

$\bf (54 + 46)(54 - 46) \\ \rm=54(54-46)+46(54-46) \\ \rm=54^2-(54 \times46)+(46 \times54)-46^2 \\ \rm =54^2-(54 \times46)+(54 \times46)-46^2 \\ = 54^2 \cancel{-2484} \: \: \cancel{+2484}-46^2 \\ \bf=54^2-46^2 \\ = 2916 -2116 \\ = \large \bf{800}$

More identities used frequently_in algebra are :

$\small\boxed{ \begin{gathered} 1. \: \rm \: (x + a)(x + b) = {x}^{2} + (a + b)x + ab \\ 2. \: \rm \: (a + b) {}^{2} = {a}^{2} + 2ab + {b}^{2} \\ 3. \: \rm \: (a + b) {}^{2} = {a}^{2} - 2ab + {b}^{2} \\ 4. \: \rm \: (a + b)(a - b) = {a}^{2} - {b}^{2} \end{gathered}}$