I'll just help quickly with a couple of expressions that are equivalent.
3(m+5+9m)
If you solve it out, you get 3m+15+27m.
Simply the expression to get 30m+15.
You can regroup to make another expression 5(6m+3) which is also equal.
difference of squares means that both the terms are square terms. (also there must be a - symbol)
for example
y^2 - 4
square root of y^2 is y
square root of 4 is +2 as well as -2
so you would factorise it like this:
(y+2)(y-2)
1. y^4 has a square root of y^2 as y^2 × y^2 is y^4.
<em>h</em><em>o</em><em>w</em><em>e</em><em>v</em><em>e</em><em>r</em><em>,</em><em> </em>-2 doesnt have a whole number square root so it is not a difference of squares.
2. 25 has a square root of 5. m^2 has a square root of m. n^4 has a square root of n^2. so this 25m^2n^4 is a square term.
1 has a square root of +1 and -1.
therefore, this one is a difference of squares. <u>(</u><u>5</u><u>m</u><u>n</u><u>^</u><u>2</u><u> </u><u>+</u><u>1</u><u>)</u><u> </u><u>(</u><u>5</u><u>mn^2</u><u> </u><u>-</u><u>1</u><u>)</u>
3. p^8 has a square root of p^4. q^4 has a square root of +q^2 and -q^2)
so it is a difference of squares. <u>(</u><u>p</u><u>^</u><u>4</u><u>+</u><u>q</u><u>^</u><u>2</u><u>)</u><u>(</u><u>p</u><u>^</u><u>4</u><u> </u><u>-</u><u>q</u><u>^</u><u>2</u><u>)</u>
4. 16x^2 is a square term as irs square root is 4x.
<em>h</em><em>o</em><em>w</em><em>e</em><em>v</em><em>e</em><em>r</em><em>,</em><em> </em>24 is not a square term.
therefore, it is not a difference of squares.
-z³ + 5k^6 + z³ -10k^6
(-z³ cancels out with z³)
5k^6 -10k^6
(then subtract)
Answer is -5k^6
