Question

\( 56 a b+14-49 a-16 b \)

Ask by Deleon Crawford. in the United States
Mar 12,2025

Upstudy AI Solution

Tutor-Verified Answer

Answer

The expression \(56ab + 14 - 49a - 16b\) can be factored as \((7a - 2)(8b - 7)\).

Solution

1. Rewrite the expression by grouping like terms: \[ 56ab + 14 - 49a - 16b = (56ab - 49a) + (-16b + 14) \] 2. Factor the first group by factoring out \(7a\): \[ 56ab - 49a = 7a(8b - 7) \] 3. Factor the second group by factoring out \(-2\): \[ -16b + 14 = -2(8b - 7) \] 4. Now, notice that both groups contain the common factor \((8b - 7)\). Factor \((8b - 7)\) out: \[ 7a(8b - 7) - 2(8b - 7) = (8b - 7)(7a - 2) \] Thus, the fully factored form of the expression is: \[ (7a - 2)(8b - 7) \]

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Simplify this solution

Beyond the Answer

To simplify the expression \( 56ab + 14 - 49a - 16b \), first, group like terms: \( 56ab - 49a - 16b + 14 \). Now, identifying any common factors among the first three terms could help. Notice that there aren't obvious factors that allow further factorization without additional context or restrictions. However, if you're looking for a straightforward expression, it simplified as it stands is \( -49a + 56ab - 16b + 14\). While it’s not always apparent, the ability to manipulate algebraic expressions like this is crucial in various scientific fields, especially physics and engineering! Simplifying expressions forms the backbone of solving equations and modeling real-world phenomena. If you’re delving into algebra, keep in mind common mistakes such as misapplying the distributive property, especially when negative signs are involved. Double-check your work by plugging in values to ensure everything balances as expected!

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