Question

3. Find the product using the identity
(x + a) (x+6) = x + (a+b)x+ ab.
a. (2x – 7y) (2x + 8y)
b. 103 x 95
c. 505 x 502
d. (5p - 79) (5p - 79)​

Answer 1

⍟ANSWERS⍟

᯽ғᴏʀᴍᴜʟᴀ᯽

• $(x + a) (x+b)$

$\:\:\:\:\:\:\:= x^2 + (a+b)x+ ab$

❤︎sᴏʟᴜᴛɪᴏɴ❤︎

1. $(2x – 7y) (2x + 8y)$

Applying the given formula, we get

$\to (2x)^2 + (-7y + 8y)2x + 7y \times 8y$

$\to 4x^2 + (y)2x + 56y^2$

$\to\ 4x^2 + 2xy + 56y^2$

2. $103\times 95$

Here,

$\:\:\:\:\: 103 \times 95$

$\to (100 + 3)\times (100 - 5)$

Applying the given formula, we get

$\to 100^2 + [3 + (- 5)]\times 100 +3\times (-5)$

$\to 10000 - 2\times 100 - 15$

$\to 10000 - 200 - 15$

$\to 9800 - 15$

$\to 9785$

3. $505\times 502$

Here,

$\:\:\:\:\: 505\times 502$

$\to (500 + 5)\times (500 + 2)$

Applying the given formula, we get

$\to 500^2 + (5 + 2)\times 500 + 5\times 2$

$\to 250000+ 7\times 500 + 10$

$\to 250000+ 3500 + 10$

$\to 250000+ 3510$

$\to 253510$

4. $(5p - 79) (5p - 79)$

Applying the given formula, we get

$\to (5p)^2 +[(- 79) + (-79)]\times 5p$

$\:\:\:\:\:+ (- 79)\times (-79)$

$\to 25p^2 - 158\times 5p + 6241$

$\to 25p^2 - 790p + 6241$

❦︎ᴀᴅᴅɪᴛɪᴏɴᴀʟ ғᴏʀᴍᴜʟᴀs❦︎

• $(a + b)^2 = a^2 + 2ab + b^2$

• $(a - b)^2 = a^2 - 2ab + b^2$

• $(x - a)(x - b)$

$\:\:\:\:\:\:\:= x^2 - (a+b)x + ab$

Answer 2

Answer:

I will tell the answer tomorrow