Subjects algebra

Term Combinations A43E46

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1. The problem asks to find combinations of terms in each table that can be combined with the term written in red above each table. 2. The red terms are: - First table: $-q$ - Second table: $3y$ - Third table: $-7x$ 3. To combine terms, we look for like terms (same variable and power) in each table that can be added or subtracted with the red term. 4. First table (red term $-q$): - Terms: $-6, 8, -(2), 2, -5x, -19, -7, 4, 2, 4x, x, 5, -x, 8x, -3$ - None of these terms contain $q$, so no combination is possible with $-q$. 5. Second table (red term $3y$): - Terms: $5y, -2y, y, 5x, 3, -y, y, -4y, 8y, 6y, -7x, 8, 9y, -5y, 2y$ - Combine like terms with $3y$: - $3y + 5y = 8y$ - $3y + (-2y) = y$ - $3y + y = 4y$ - $3y + (-y) = 2y$ - $3y + (-4y) = -y$ - $3y + 8y = 11y$ - $3y + 6y = 9y$ - $3y + 9y = 12y$ - $3y + (-5y) = -2y$ - $3y + 2y = 5y$ 6. Third table (red term $-7x$): - Terms: $4, 3x, y, -y, -x, 3z, -14, -z, 9x, 21, 8, 5x, 4y$ - Combine like terms with $-7x$: - $-7x + 3x = -4x$ - $-7x + (-x) = -8x$ - $-7x + 9x = 2x$ - $-7x + 5x = -2x$ 7. Summary of combinations: - With $-q$: none - With $3y$: $8y, y, 4y, 2y, -y, 11y, 9y, 12y, -2y, 5y$ - With $-7x$: $-4x, -8x, 2x, -2x$ Final answer: - No combinations with $-q$. - Combinations with $3y$ are $8y, y, 4y, 2y, -y, 11y, 9y, 12y, -2y, 5y$. - Combinations with $-7x$ are $-4x, -8x, 2x, -2x$.