A few expanding and factorizing questions..?

Question

Can someone please help me with answers for a few simple expressions?:

1) Expand 4(x-1)(2x-3)

2) Expand -7(x+3)^2

3) Factorize 98x^2-72y^2

And a few harder ones...:

Factorize:

1) (x+3)^2-(x-1)^2

2) 2(x+1)^2+5(x+1)+2

It would be most appreciated if the answers were explained abit but I don't mind plain answers if you can't be bother. Thanks. :)

Answer 1

1)

(4x-4)(2x-3)

8x^2-12x-8x+12

8x^2-20x+12

2)

-7(X^2+6x+9)    as (a+b)^2=a^2+2ab+b^2

-7x^2_42x-63

3)

98x^2-72y^2

taking 2 common

2(49x^2-36y^2)

2(7x-6y)(7x+6y)  as (x^2-y^2- (x-y)(x+y)

harder

1)

{(X+3)+(x-1)}{(x+3)-(x-1)}    as (x^2-y^2- (x-y)(x+y)

(x+3+x-1)(x+3-x-1)

(2x+4)(2)

2(x+2)(2)

4(x+2)

Answer 2

1) First, just multiply the 4 by each term in (x-1) (the x and the 1). Then, use that result and the (2x-3) term with the FOIL method (multiply the First terms, then Outer terms, then Inner terms, then Last terms, and add them all up, in order).

So it would be:

4(x-1)(2x-3)

(4x-4)(2x-3)

8x²-12x-8x+12

8x²-20x+12

2) First write (x+3)² as (x+3)(x+3). Then use the same method as above to completely expand.

3) First, we see that the first term's variable is x and the secon term's variable is y. Therefore, these cannot be factored and must be left alone. So we turn to the coefficients. What factors do 98 and 72 have in common? Obviously, 2. So factor out the 2 like so:

98x² - 72y² = 2(49x² - 36y²)

Do 49 and 36 have any common factors? Well, the factors of 49 are just 1, 7, and 7. The factors of 36 are 2, 2, 3, and 3. Nothing in common, so we're done, and the answer is:

2(49x² - 36y²)

-IMP ;) :)