Subjects algebra

Algebra Terms 3A4D09

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1. **Problem:** Given the algebraic expression $$4x^2 - 3x + 2x^2 - 7x - 5$$ 2. **Step 1: Identify the terms (Suku-suku) in the expression.** The terms are the parts separated by plus or minus signs: $$4x^2, -3x, 2x^2, -7x, -5$$ 3. **Step 2: Identify like terms (Suku-suku yang sejenis).** Like terms have the same variable and exponent: - $$4x^2$$ and $$2x^2$$ are like terms. - $$-3x$$ and $$-7x$$ are like terms. - $$-5$$ is a constant term. 4. **Step 3: Determine the degree (Derajat) of the algebraic expression.** The degree is the highest exponent of the variable in the expression. Here, the highest exponent is 2 (from $$x^2$$ terms), so the degree is 2. 5. **Step 4: Simplify the algebraic expression by combining like terms.** Combine $$4x^2$$ and $$2x^2$$: $$4x^2 + 2x^2 = \cancel{4x^2} + \cancel{2x^2} = 6x^2$$ Combine $$-3x$$ and $$-7x$$: $$-3x - 7x = \cancel{-3x} - \cancel{7x} = -10x$$ The constant term remains $$-5$$. So, the simplified expression is: $$6x^2 - 10x - 5$$ **Final answers:** - a. Terms: $$4x^2, -3x, 2x^2, -7x, -5$$ - b. Like terms: $$4x^2, 2x^2$$ and $$-3x, -7x$$ - c. Degree: 2 - d. Simplified expression: $$6x^2 - 10x - 5$$