1. ## Factorise and simplify

2. I. What is x^2 - y^2?
II. a^2 + 2ab + b^2 = (a + b)^2. What is a? What is b?

3. Hello turbo,

(I) $\displaystyle 2x^2-2y^2$

Always look for common monimial factors over the terms of the polynomial. In this case, 2 is a common factor. Now, we have

$\displaystyle 2(x^2-y^2)$

You should recognize the difference of two squares. You should memorize the pattern for factoring it. I'll leave the finish for you.

(II) $\displaystyle 64x^2+16xy+y^2$

You may or may not recognize this as a perfect square trinomial, but you should see that the first and last terms are perfect squares. You should also memorize a factorization pattern for this.

$\displaystyle x^2+2xy+y^2=(x+y)^2$

You can do the rest.

(III) $\displaystyle 36x^2z-21xyz+15yxz-6y^2z$

You should notice that the two middle terms are like terms and can be combined (even though the variables are in a different order).

$\displaystyle 36x^2z-6xyz-6y^2z$

Now, find your monomial factor of 6z and factor it out.

$\displaystyle 6z(6x^2-xy-y^2)$

See if you can finish factoring the trinomial.