Question

(4x to the 4th power + 4x to the 3rd power - 1) - (5x to the 2nd power - 9x + 6)

Answer 1

(x + 9)(x + 5)

Answer 2

(4k + 7)(2k - 3)

Answer 3

(a - 1)(a - 12)

Answer 4

(a - 8)(a - 12)

Answer 5

To simplify the expression \((4x^4 + 4x^3 - 1) - (5x^2 - 9x + 6)\), you can start by distributing the negative sign across the second set of parentheses:

\[
= 4x^4 + 4x^3 - 1 - 5x^2 + 9x - 6
\]

Now, combine like terms:

1. The term \(4x^4\) has no like terms, so it remains as \(4x^4\).
2. The term \(4x^3\) also has no like terms, so it remains as \(4x^3\).
3. The term \(-5x^2\) has no like terms, so it stays as \(-5x^2\).
4. The term \(9x\) has no like terms, so it remains as \(9x\).
5. Combine the constant terms: \(-1 - 6 = -7\).

Putting it all together, the simplified expression is:

\[
4x^4 + 4x^3 - 5x^2 + 9x - 7
\]

Answer 6

To expand the expression \((x + 9)(x + 5)\), you can use the distributive property, also known as the FOIL method (First, Outside, Inside, Last).

Here's how it works step-by-step:

1. **First**: Multiply the first terms:
\[
x \cdot x = x^2
\]

2. **Outside**: Multiply the outer terms:
\[
x \cdot 5 = 5x
\]

3. **Inside**: Multiply the inner terms:
\[
9 \cdot x = 9x
\]

4. **Last**: Multiply the last terms:
\[
9 \cdot 5 = 45
\]

Now, combine all these results:
\[
x^2 + 5x + 9x + 45
\]

Combine the like terms \(5x\) and \(9x\):
\[
x^2 + 14x + 45
\]

So, the expanded form of \((x + 9)(x + 5)\) is:
\[
\boxed{x^2 + 14x + 45}
\]

Answer 7

To expand the expression \((4k + 7)(2k - 3)\), you can use the distributive property (also known as the FOIL method). Here’s how to do it step-by-step:

1. **First**: Multiply the first terms:
\[
4k \cdot 2k = 8k^2
\]

2. **Outside**: Multiply the outer terms:
\[
4k \cdot (-3) = -12k
\]

3. **Inside**: Multiply the inner terms:
\[
7 \cdot 2k = 14k
\]

4. **Last**: Multiply the last terms:
\[
7 \cdot (-3) = -21
\]

Now, combine all these results:
\[
8k^2 - 12k + 14k - 21
\]

Next, combine the like terms \(-12k\) and \(14k\):
\[
8k^2 + 2k - 21
\]

So, the expanded form of \((4k + 7)(2k - 3)\) is:
\[
\boxed{8k^2 + 2k - 21}
\]

Answer 8

To expand the expression \((a - 1)(a - 12)\), you can use the distributive property (also known as the FOIL method). Here’s how to do it step-by-step:

1. **First**: Multiply the first terms:
\[
a \cdot a = a^2
\]

2. **Outside**: Multiply the outer terms:
\[
a \cdot (-12) = -12a
\]

3. **Inside**: Multiply the inner terms:
\[
-1 \cdot a = -a
\]

4. **Last**: Multiply the last terms:
\[
-1 \cdot (-12) = 12
\]

Now, combine all these results:
\[
a^2 - 12a - a + 12
\]

Next, combine the like terms \(-12a\) and \(-a\):
\[
a^2 - 13a + 12
\]

So, the expanded form of \((a - 1)(a - 12)\) is:
\[
\boxed{a^2 - 13a + 12}
\]

Answer 9

To expand the expression \((a - 8)(a - 12)\), you can use the distributive property (FOIL method). Here’s how to do it step-by-step:

1. **First**: Multiply the first terms:
\[
a \cdot a = a^2
\]

2. **Outside**: Multiply the outer terms:
\[
a \cdot (-12) = -12a
\]

3. **Inside**: Multiply the inner terms:
\[
-8 \cdot a = -8a
\]

4. **Last**: Multiply the last terms:
\[
-8 \cdot (-12) = 96
\]

Now, combine all these results:
\[
a^2 - 12a - 8a + 96
\]

Next, combine the like terms \(-12a\) and \(-8a\):
\[
a^2 - 20a + 96
\]

So, the expanded form of \((a - 8)(a - 12)\) is:
\[
\boxed{a^2 - 20a + 96}
\]