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To factor the quadratic expression \( b^2 + 8b + 7 \), you need to find two numbers that multiply to give the constant term (7) and add to give the coefficient of the middle term (8). The two numbers that satisfy these conditions are 7 and 1 because: - 7 * 1 = 7 - 7 + 1 = 8 Now, you can write the quadratic expression as a product of two binomials: \[ b^2 + 8b + 7 = (b + 7)(b + 1) \] So, the factored form of \( b^2 + 8b + 7 \) is \((b + 7)(b + 1)\).
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