Question

factor: 64- a^2+2ab-b^2

Answer 1

64- a^2+2ab-b^2
= 64 - (a^2 - 2ab + b^2)
Apply the identity \((a\pm b)^2 = a^2 \pm 2ab + b^2\)
= 64 - ( a-b)^2
= 8^2 - (a-b)^2
Apply the identity \(a^2 - b^2 = (a+b)(a-b)\)
= [8-(a-b)][8+(a-b)]
Simplify the things in the bracket, can you do it?

Answer 2

thank you so much! so it would be (8-a+b) and (8+a-b)?

Answer 3

Yup :)

Answer 4

you're amazing! can I ask you one more?

Answer 5

I'm not, but you can ask :)

Answer 6

factor completely: 243x^5-y^15

Answer 7

Hmm... not sure for this one :|
\[243x^5-y^{15} \]\[=(3x)^5-(y^{3})^5 \]\[=(3x-y^3)[(3x)^4+(3x)^3(y^3)+(3x)^2(y^3)^2+(3x)(y^3)^3+(y^3)^4]\]\[=(3x-y^3)(81x^4+27x^3y^3+9x^2y^6+3xy^9+y^{12})\]

Answer 8

i did it the same way! perfect thank you thank you!

Answer 9

welcome :)