Ask a New Question
Menu

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

9 answers

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:

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

(x + 9)(x + 5)

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: \[ \boxed{x^2 + 14x + 45} \]

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

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: \[ \boxed{8k^2 + 2k - 21} \]

(a - 1)(a - 12)

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: \[ \boxed{a^2 - 13a + 12} \]

(a - 8)(a - 12)

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: \[ \boxed{a^2 - 20a + 96} \]