Question

factor this sum of cubes.
8x³ + 27
(?x + )( x² − 6x + )
hint: a³ ± b³ = (a ± b)(a² ∓ ab + b²)

Explanation:

Step1: Identify \(a\) and \(b\) in sum of cubes

The sum of cubes formula is \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\). For \(8x^3+27\), we can rewrite \(8x^3=(2x)^3\) and \(27 = 3^3\). So \(a = 2x\) and \(b = 3\).

Step2: Apply the sum of cubes formula

Using the formula \(a^3 + b^3=(a + b)(a^2 - ab + b^2)\), substitute \(a = 2x\) and \(b = 3\):

• The first factor is \(a + b=2x + 3\).
• The second factor is \(a^2 - ab + b^2=(2x)^2-(2x)(3)+3^2 = 4x^2-6x + 9\).

So comparing with \((\square x+\square)(\square x^2 - 6x+\square)\), we have:

• The coefficient of \(x\) in the first factor: \(2\)
• The constant term in the first factor: \(3\)
• The coefficient of \(x^2\) in the second factor: \(4\)
• The constant term in the second factor: \(9\)

Answer:

The filled - in form is \((2x + 3)(4x^2 - 6x + 9)\), so the values in the boxes (from left to right, top to bottom) are \(2\), \(3\), \(4\), \(9\).