Question

find the value of 105 into 95 by using the identity o

f algebraic expression​

Answer 1

$\rule{400}4$

☆ ANSWER:-

▪︎ To Find:-

• The value of 105×95.

▪︎ ID Used:-

$\tt\leadsto(a + b)( a - b) = { a}^{2} - {b}^{2} .$

$\rule{400}2$

▪︎ Now here,

• 105 can be written as 100+5.

• And 95 can be written as 100-5.

$\rule{400}2$

▪︎ So lets find the product:-

$\tt\mapsto105 \times 95 \\ \\ \sf = (100 + 5) \times (100 - 5) \\ \\ \sf = (100 + 5)(100 - 5) \\ \\ \sf = (100) {}^{2} - (5) {}^{2} \\ \\\sf(by \: usi ng \: id) \\ \\ \sf = 10000 - 25 \\ \\ \sf \large\blue{\fbox{= 9975.}}$

$\therefore$ 105×95 = 9975.

$\rule{400}4$

▪︎ More algebraic IDs:-

$\tt\leadsto(a + b) {}^{2} = {a}^{2} + {b}^{2} + 2ab. \\ \\ \tt\leadsto(a - b) {}^{2} = {a}^{2} + {b}^{2} - 2ab. \\ \\ \tt\leadsto {a}^{2} - {b}^{2} = (a + b)( a - b). \\ \\ \tt\leadsto(x + a)(x + b) = {x}^{2} + (a + b)x + ab.$

$\rule{400}4$

Answer 2

✯✯ QUESTION ✯✯

Find the value of 105 into 95 by using the identity .

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✰✰ ANSWER ✰✰

$\longrightarrow{105\times{95}}$

$\longrightarrow{105=100+5}$

$\longrightarrow{95=100-5}$

$\longrightarrow{100+5\times100-5}$

➥Using Identity : -

$\longrightarrow{\small{\bold{\bold{\bold{\green{\sf{(a+b)(a-b)={a}^{2}-{b}^{2}}}}}}}}$

$\longrightarrow{{(100)}^{2}-{(5)}^{2}}$

$\longrightarrow{\textbf{10000-25}}$

$\longrightarrow{\large{\boxed{\bold{\bold{\purple{\sf{Answer=9975}}}}}}}$

_______________________

➥Some More Identities : -

★(a-b)²=a²+b²-2ab

★(a+b)²=a²+b²+2ab

★(x+a)(x+b)=x²+(a+b)x+ab