Question

30 points! please help!

Answer 1

Explanation:

Answer 2

Therefore

15.

`25c^(2)-9`

16.

`(y+8)(y+1)`

17.

`(x-3y)(x-7y)`

Explanation:

15.

`(5c^(2) +3)(5c^(2)-3)`

Using the Identity (a + b)(a - b) = (a² - b²) we get

Consider here a = 5c and b = 3 then we will have

`((5c)^(2) -(3)^(2))=25c^(2)-9` .....as required

16.

`y^(2)+9y+8`

Here Factorize 8 such that sum up to be 9

∴ 8 × 1 = 8 and 8 + 1 =9

`y^(2)+9y+8\\y^(2)+8y+y+8\\y(y+8)+1(y+8)\\(y+8)(y+1)` ... as required

17.

`x^(2)-10xy+21y^(2)`

Here Factorize 21 such that sum up to be -10

∴ -3 × -7 = + 21 and -3 - 7 = - 10

`x^(2)-10xy+21y^(2)\\x^(2)-3xy-7xy+21y^(2)\\x(x-3y)-7y(x-3y)\\(x-3y)(x-7y)` ........as required

Therefore

15.

`25c^(2)-9`

16.

`(y+8)(y+1)`

17.

`(x-3y)(x-7y)`