Question

16(a+b)² - 9(a-b)²

Answer 1

Write 16(a+b)^2 as { 4(a+b) }^2 = {4a + 4b}^2.
Do the same with 9(a-b)^2

Then you have the difference of two squares: x^2 - y^2 = (x+y)(x-y)

Answer 2

@Hero

Answer 3

@ranga [4(a+b)]² - [3(a-b)]²

Answer 4

Yes. [4(a+b)]² - [3(a-b)]² = [4a + 4b]² - [3a - 3b]²
This is of the form x² - y² = (x + y)(x - y)
Simplify.

Answer 5

wait

Answer 6

so do i get 3a and 3b with 4a and 4b ?

Answer 7

Your x is 4a + 4b
y is 3a - 3b
x+y = ?
x-y = ?
multiply the two.

Answer 8

?

Answer 9

Use the identity: x² - y² = (x + y)(x - y)
Compare it to: [4a + 4b]² - [3a - 3b]²
x = 4a + 4b
y = 3a - 3b

You just need to find x+y and multiply it with x-y

Answer 10

im doing first time so confused

Answer 11

Well, using the identity will simplify the algebra. But if you don't want to use it then expand [4a + 4b]² - [3a - 3b]² and simplify.

Answer 12

can u do and show me

Answer 13

This is the LONG method without using the identity:
[4a + 4b]² = (4a)² + (4b)² + 2(4a)(4b) = 16a² + 16b² + 32ab
[3a - 3b]² = (3a)² + (3b)² - 2(3a)(3b) = 9a² + 9b² + 18ab
[4a + 4b]² - [3a - 3b]² = (16-9)a² + (16-9)b² + (32+18)ab = 7a² + 7b² + 50ab
= 7a² + 49ab + ab + 7b^2 = 7a(a + 7b) + b(a + 7b) = (7a+b)(a+7b)

Answer 14

Using the identity: x² - y² = (x + y)(x - y)
Compare [4a + 4b]² - [3a - 3b]² to above.
x = 4a + 4b
y = 3a - 3b
x² - y² = (x + y)(x - y) = (4a + 4b + 3a - 3b) * (4a + 4b - 3a + 3b)
= (7a+b)(a+7b)

Answer 15

In two replies ago, in the third line it should be -18ab not +18ab. But the final answer is correct.