Question

1. (15+k²)²2. (m²-3n)²3. (m⁴-n³)²4.​

Answer 1

1. (15+k^2)^2
225+30k^2+k^4
k^4+30k^2+225
2.(m^2-3n)^2
(m^2)^2-2m^2•3n+(3n)^2
m^4-6m^2n+9n^2
3. (m^4-n^3)^2
(m^4)^2-2m^4n^3+(n^3)^2
m^8-2m^4n^3+n^6
4. (5a^4-2a^7)^2
25a^8-20a^11+4a^14
4a^14-20a^11+25a^8

Answer 2

1) (15+k^2)^2=225+30k^2+k^4=k^4+30k^2+225
2) (m^2-3n)^2=(m^2)^2-2m^2*3n+(3n)^2=m^4-6m^2n+9n^2
3) (m^4-n^3)^2=(m^4)^2-2m^4n^3+(n^3)^2=m^8-2m^4n^3+n^6
4) (5a^4-2a^7)^2=25a^8-20a^11+4a^14=4a^14-20a^11+25a^8

Answer 3

It seems like you want to expand these algebraic expressions. Let's expand each of them:

1. $(15 + k^2)^2$ To expand this expression, you can use the FOIL (First, Outer, Inner, Last) method. Here's how it expands:

$$(15 + k^2)^2 = (15 + k^2)(15 + k^2)$$

Now, apply the FOIL method:

$$= 15 \cdot 15 + 15 \cdot k^2 + k^2 \cdot 15 + k^2 \cdot k^2 = 225 + 30k^2 + k^4$$

So, $(15 + k^2)^2 = 225 + 30k^2 + k^4$.

2. $(m^2 - 3n)^2$ To expand this expression, again use the FOIL method:

$$(m^2 - 3n)^2 = (m^2 - 3n)(m^2 - 3n)$$

Now, apply the FOIL method:

$$= m^2 \cdot m^2 - m^2 \cdot 3n - 3n \cdot m^2 + 3n \cdot 3n = m^4 - 3m^2n - 3m^2n + 9n^2 = m^4 - 6m^2n + 9n^2$$

So, $(m^2 - 3n)^2 = m^4 - 6m^2n + 9n^2$.

3. $(m^4 - n^3)^2$ Once again, apply the FOIL method:

$$(m^4 - n^3)^2 = (m^4 - n^3)(m^4 - n^3)$$

FOIL:

$$= m^4 \cdot m^4 - m^4 \cdot n^3 - n^3 \cdot m^4 + n^3 \cdot n^3 = m^8 - m^4n^3 - m^4n^3 + n^6 = m^8 - 2m^4n^3 + n^6$$

So, $(m^4 - n^3)^2 = m^8 - 2m^4n^3 + n^6$.

These are the expanded forms of the given expressions.