Please help me?

Question

I do not understand these questions.

1) Factor completely
25x^2-49

2) Factor completely
x^2+12x+36

3)Multiply
(5a-3b)^2

4) factor completely

4x^2+5xy+32x+40y


If you can help I would really like it...please show me work or give me a site that will help...thanks

Answer 1

1. (5x-7)(5x+7)

2. (x+6)(x+6)

3. 25a^2 - 30ab + 9b^2

4. (4x+y)(x+8)

Answer 2

25x^2-49
=(5x-7)^2
they're both squares, so you can factor out the power of 2

x^2+12x+36
=(x+6)^2

to check it, expand it back again
(x+6)^2
= (x+6)(x+6)
= x^2 + 6x + 6x + 36
= x^2 + 12x + 36

(5a-3b)^2 - watch for the minus sign in this one
=(5a-3b)(5a-3b)
=25a^2 -15ab -15ab + 9b^2
= 25a^2 - 30ab + 9b^2
but you should format it so that the things with ^2 are at the front
= 25a^2 + 9b^2 - 30ab

factor: 4x^2+5xy+32x+40y
this one will turn into a quadratic thing in the format (a+b)(c+d)
=4x^2 + 32x + 5xy + 40y
=4x(x+8) + 5y(x+8)
* in the next step we take out the common factor of (x+8)
=(x+8)(4x+5y)

I'm not entirely sure about those last two, but you can expand/factorise them to check it.

Answer 3

1) 5x - 7).(5x + 7)
2) (x + 6).(x + 6)
3) (5a - 3b).(5a - 3b)
= 25a² - 30ab + 9b²
4) 4x.(x + 8) + 5y.(x + 8)
= (x + 8).(4x + 5y)