Question

Hey guys help me to answer this question​

Answer 1

$\textsf{\large{\underline{Solution}:}}$

We have to evaluate 103 x 107 using identity.

We can write the product as:

$\rm = (100 + 3)(100 + 7)$

Let us assume that:

$\rm: \longmapsto x = 100$

$\rm: \longmapsto a = 3$

$\rm: \longmapsto b= 7$

Therefore, the product becomes:

$\rm = (x + a)(x + b)$

Using identity, we get:

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

Substituting the values in the expression, we get:

$\rm = {100}^{2} + (3 + 7) \times 100 + 3 \times 7$

$\rm = 10000 + 1000 +21$

$\rm = 11021$

Therefore:

$\rm: \longmapsto 103 \times 107 = 11021$

★ Which is our required answer.

$\textsf{\large{\underline{More Identities To Know}:}}$

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab

Answer 2

Answer:

$\large\bf{\underline{\green{VERIFIED✔}}}$

Step-by-step explanation:

$[tex]\textsf{\large{\underline{Solution}:}}$

We have to evaluate 103 x 107 using identity.

We can write the product as:

$\rm = (100 + 3)(100 + 7)$

Let us assume that:

$\rm: \longmapsto x = 100$

$\rm: \longmapsto a = 3$

$\rm: \longmapsto b= 7$

Therefore, the product becomes:

$\rm = (x + a)(x + b)$

Using identity, we get:

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

Substituting the values in the expression, we get:

$\rm = {100}^{2} + (3 + 7) \times 100 + 3 \times 7$

$\rm = 10000 + 1000 +21$

$\rm = 11021$

Therefore:

$\rm: \longmapsto 103 \times 107 = 11021$

★ Which is our required answer.

$\textsf{\large{\underline{More Identities To Know}:}}$

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)³ = a³ + 3ab(a + b) + b³

(a - b)³ = a³ - 3ab(a - b) - b³

a³ + b³ = (a + b)(a² - ab + b²)

a³ - b³ = (a - b)(a² + ab + b²)

(x + a)(x + b) = x² + (a + b)x + ab

(x + a)(x - b) = x² + (a - b)x - ab

(x - a)(x + b) = x² - (a - b)x - ab

(x - a)(x - b) = x² - (a + b)x + ab[/tex]