To write the expanded form of the trinomial \(10x^2 - 61x + 72\) that can be used to factor the expression by grouping, you would need to multiply the coefficient of the quadratic term by the constant term, which gives you \(10 \times 72 = 720\).
Next, you need to find two numbers that multiply to 720 and add up to the coefficient of the linear term, which is -61. These numbers are -8 and -90 since (-8) * (-90) = 720 and (-8) + (-90) = -98, not -61.
Therefore, the trinomial can be rewritten as:
\[10x^2 - 8x - 90x + 72\]
Now, you can group the terms:
\[(10x^2 - 8x) + (-90x + 72)\]
Factor out the GCF from each group:
\[2x(5x - 4) - 18(5x - 4)\]
Now, you can factor out the common binomial factor:
\[(2x - 18)(5x - 4)\]
So, the expanded form that can be used to factor the expression by grouping is \((2x - 18)(5x - 4)\).
