Pregunta
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\( 2(4y-z)(4y+z) \)
Solución
Factor the expression \( 32y^{2}-2z^{2} \).
Factor the expression by following steps:
- step0: Factor:
\(32y^{2}-2z^{2}\)
- step1: Factor the expression:
\(2\left(16y^{2}-z^{2}\right)\)
- step2: Factor the expression:
\(2\left(4y-z\right)\left(4y+z\right)\)
The fully factored form of \(32y^{2}-2z^{2}\) is \(2(4y-z)(4y+z)\).
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Simplifique esta solución Bonus Knowledge
To factorise the expression \( 32 y^{2} - 2 z^{2} \), we can start by factoring out the greatest common factor, which is 2: \[ 2(16y^{2} - z^{2}) \] Next, we notice that \( 16y^{2} - z^{2} \) is a difference of squares. The difference of squares can be factored using the formula \( a^2 - b^2 = (a - b)(a + b) \). Here, \( a = 4y \) and \( b = z \): \[ 2(4y - z)(4y + z) \] Thus, the fully factorised form of the expression \( 32 y^{2} - 2 z^{2} \) is: \[ 2(4y - z)(4y + z) \]
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