Question
Factorise fully 1.1.1. \( 1+y^{2}=5 \) 1.12. \( 6 m+3 m^{2}=9 \)
Ask by Ford Weber. in South Africa
Mar 20,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The factorized forms are:
1. \( y = \pm 2 \)
2. \( 3(m - 1)(m + 3) = 0 \)
Solution
To factorize the given equations, we need to rearrange them to the form of a quadratic equation and then factorize them.
1.1.1. \(1+y^{2}=5\)
Rearrange the equation to the form of a quadratic equation:
\(y^{2} = 5 - 1\)
\(y^{2} = 4\)
Factorize the quadratic equation:
\(y^{2} = 2^{2}\)
\(y = \pm 2\)
Therefore, the factorized form of the equation \(1+y^{2}=5\) is \(y = \pm 2\).
1.1.2. \(6m + 3m^{2} = 9\)
Rearrange the equation to the form of a quadratic equation:
\(3m^{2} + 6m - 9 = 0\)
Factorize the quadratic equation:
\((3m - 3)(m + 3) = 0\)
\(3(m - 1)(m + 3) = 0\)
Therefore, the factorized form of the equation \(6m + 3m^{2} = 9\) is \(3(m - 1)(m + 3) = 0\).
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Simplify this solution Mind Expander
To fully factorise \(1 + y^{2} = 5\), we first rearrange it to \(y^{2} = 4\) and then take the square root: \(y = \pm 2\). This means the expression can be rewritten as \((y - 2)(y + 2) = 0\), factoring down to these two linear factors. For \(6m + 3m^{2} = 9\), we can start by moving all terms to one side to get \(3m^{2} + 6m - 9 = 0\). Factoring out a common factor of 3 gives us \(3(m^{2} + 2m - 3) = 0\). The quadratic can be further factorised into \((m + 3)(m - 1) = 0\), providing the fully factorised form \(3(m + 3)(m - 1) = 0\).
