Simplify Grade 10 Algebraic Expressions

Recent questions

• How do you add fractions together?

  To add fractions, you first need to find a common denominator. This involves identifying the denominators of the fractions you want to add and determining the least common multiple (LCM) of those denominators. Once you have the common denominator, you can adjust each fraction by multiplying both the numerator and denominator by the necessary factors to make the denominators equal. After adjusting, you can add the numerators together while keeping the common denominator. Finally, simplify the resulting fraction if possible by reducing it to its lowest terms.

• What is a trinomial in math?

  A trinomial is a polynomial that consists of three terms. It typically takes the form \( ax^2 + bx + c \), where \( a \), \( b \), and \( c \) are constants, and \( x \) is a variable. Trinomials can be factored into the product of two binomials, which is a common technique in algebra. For example, the trinomial \( x^2 - x - 6 \) can be factored into \( (x + 2)(x - 3) \) by finding two numbers that multiply to the constant term (-6) and add up to the coefficient of the middle term (-1). This factoring process is essential for solving quadratic equations and simplifying expressions.

• What is a common denominator?

  A common denominator is a shared multiple of the denominators of two or more fractions. It allows for the addition or subtraction of fractions by providing a uniform base for comparison. To find the lowest common denominator (LCD), you identify all unique factors from the denominators and combine them. For instance, if you have fractions with denominators of 3 and 5, the common denominator would be 15, as it is the smallest number that both denominators can divide into without leaving a remainder. Using a common denominator simplifies the process of performing arithmetic operations on fractions.

• How do you simplify a fraction?

  Simplifying a fraction involves reducing it to its simplest form, where the numerator and denominator have no common factors other than 1. To simplify a fraction, you can start by factoring both the numerator and the denominator to identify any common factors. Once you find these common factors, you can cancel them out from both the numerator and the denominator. For example, if you have the fraction \( \frac{8}{12} \), you can factor it to \( \frac{2 \times 4}{3 \times 4} \) and then cancel the common factor of 4, resulting in \( \frac{2}{3} \). This process ensures that the fraction is expressed in its most reduced form.

• What does it mean to factor an expression?

  Factoring an expression means breaking it down into simpler components, or factors, that when multiplied together give the original expression. This process is particularly useful in algebra for simplifying expressions, solving equations, and finding roots. For example, the expression \( x^2 - x - 6 \) can be factored by identifying two numbers that multiply to -6 (the constant term) and add to -1 (the coefficient of the middle term). In this case, the numbers 2 and -3 work, allowing us to express the trinomial as \( (x + 2)(x - 3) \). Factoring is a fundamental skill in algebra that aids in various mathematical operations and problem-solving techniques.