Simplify the following algebraic expressions.

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Here are the solutions for questions 1 and 2. 1. Simplify the following expressions: 1.1 5a + 4c − 3a + c + 2 − 4c + 4 Step 1: Group like terms. (5a − 3a) + (4c + c − 4c) + (2 + 4) Step 2: Combine like terms. 2a + c + 6 The simplified expression is 2a + c + 6. 1.2 −3xy + x + 2y + 4xy + 3x − 2xy + y Step 1: Group like terms. (−3xy + 4xy − 2xy) + (x + 3x) + (2y + y) Step 2: Combine like terms. (−3+4−2)xy + (1+3)x + (2+1)y −xy + 4x + 3y The simplified expression is -xy + 4x + 3y. 1.3 2a² + 4a + 7 − 3a² − 2a + 7 Step 1: Group like terms. (2a² − 3a²) + (4a − 2a) + (7 + 7) Step 2: Combine like terms. −a² + 2a + 14 The simplified expression is −a² + 2a + 14. 1.4 3ab + a − 6ab + 6a + b − 4a − 2b Step 1: Group like terms. (3ab − 6ab) + (a + 6a − 4a) + (b − 2b) Step 2: Combine like terms. −3ab + (1+6−4)a + (1−2)b −3ab + 3a − b The simplified expression is −3ab + 3a − b. 1.5 −4x²y − 5xy² − 2xy + 3xy − 6xy² − x²y Step 1: Group like terms. (−4x²y − x²y) + (−5xy² − 6xy²) + (−2xy + 3xy) Step 2: Combine like terms. (−4−1)x²y + (−5−6)xy² + (−2+3)xy −5x²y − 11xy² + xy The simplified expression is −5x²y - 11xy² + xy. 2. Simplify the following and write your answers in descending powers: 2.1 3a − 5a² + 4a + a² − 5a Step 1: Group like terms. (−5a² + a²) + (3a + 4a − 5a) Step 2: Combine like terms. (−5+1)a² + (3+4−5)a −4a² + 2a The simplified expression in descending powers is −4a² + 2a. 2.2 4a² + 3a − 2 − 4a + a² − 3 Step 1: Group like terms. (4a² + a²) + (3a − 4a) + (−2 − 3) Step 2: Combine like terms. (4+1)a² + (3−4)a + (−2−3) 5a² − a − 5 The simplified expression in descending powers is 5a² − a − 5. 2.3 ab + 6a² + 5b² − 2a² − 4ab − b² + 3a² Step 1: Group like terms. (6a² − 2a² + 3a²) + (5b² − b²) + (ab − 4ab) Step 2: Combine like terms. (6−2+3)a² + (5−1)b² + (1−4)ab 7a² + 4b² − 3ab Step 3: Arrange in descending powers (typically by the first variable, 'a'). 7a² − 3ab + 4b² The simplified expression in descending powers is 7a² − 3ab + 4b². 2.4 6a − 2 + a² − a − 5 − 4a² + 3a + 4 Step 1: Group like terms. (a² − 4a²) + (6a − a + 3a) + (−2 − 5 + 4) Step 2: Combine like terms. (1−4)a² + (6−1+3)a + (−2−5+4) −3a² + 8a − 3 The simplified expression in descending powers is −3a² + 8a − 3. 2.5 2a² + 4a³ − a² − 3a² + a + 2a² − 6a³ + a Step 1: Group like terms. (4a³ − 6a³) + (2a² − a² − 3a² + 2a²) + (a + a) Step 2: Combine like terms. (4−6)a³ + (2−1−3+2)a² + (1+1)a −2a³ + 0a² + 2a −2a³ + 2a The simplified expression in descending powers is −2a³ + 2a.

Simplify the following algebraic expressions.

Step-by-step solution

Part 1.1· 2 steps

Group like terms.

Combine like terms.

Part 1.2· 2 steps

Group like terms.

Combine like terms.

Part 1.3· 2 steps

Group like terms.

Combine like terms.

Part 1.4· 2 steps

Group like terms.

Combine like terms.

Part 1.5· 2 steps

Group like terms.

Combine like terms.

Part 2.1· 2 steps

Group like terms.

Combine like terms.

Part 2.2· 2 steps

Group like terms.

Combine like terms.

Part 2.3· 3 steps

Group like terms.

Combine like terms.

Arrange in descending powers (typically by the first variable, 'a').

Part 2.4· 2 steps

Group like terms.

Combine like terms.

Part 2.5· 2 steps

Group like terms.

Combine like terms.

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