Factorization Methods in Algebra

Grouping = Factoring out common factors from groups of terms Difference of Squares = Factoring an expression of the form a² - b² Trinomial Factorization (Quadratic Factorization) = Factoring expressions in the form ax² + bx + c Perfect Square Trinomial = Factoring an expression of the form a² + 2ab + b² or a² - 2ab + b²

10a² - 15a = 5a(2a - 3) 24x³y² + 16x²y = 8x²y(3xy + 2) 12x² + 18x = 6x(2x + 3) 9xy - 6x² = 3x(3y - 2x)

Identify the GCF of all terms = Step 1 Write the remaining terms inside the parentheses = Step 3 Factor out the GCF = Step 2 Check by expanding = Step 4

<p>12x²y + 18xy² = 6xy 6x + 9 = 3 10a² - 15a = 5a 9xy - 6x² = 3x</p> Signup and view all the answers

<p>3x(3y - 2x) = 9xy - 6x² 6x(2x + 3) = 12x² + 18x 8x²y(3xy + 2) = 24x³y² + 16x²y 5a(2a - 3) = 10a² - 15a</p> Signup and view all the answers

<p>ax + ay + bx + by = (a + b)(x + y) 3x² + 6x + 2x + 4 = (3x + 2)(x + 2) 2m² + 8m + 3m + 12 = (2m + 3)(m + 4) 4c² + 12c + 7c + 21 = (4c + 7)(c + 3)</p> Signup and view all the answers

<p>Group the terms into two pairs = Step 1 Factor out the GCF from each pair = Step 2 Check by expanding = Step 4 Factor out the common binomial factor = Step 3</p> Signup and view all the answers

<p>(ax + ay) + (bx + by) = a(x + y) + b(x + y) (3x² + 6x) + (2x + 4) = 3x(x + 2) + 2(x + 2) (2m² + 8m) + (3m + 12) = 2m(m + 4) + 3(m + 4) (4c² + 12c) + (7c + 21) = 4c(c + 3) + 7(c + 3)</p> Signup and view all the answers

<p>a(x + y) + b(x + y) = (x + y) 3x(x + 2) + 2(x + 2) = (x + 2) 2m(m + 4) + 3(m + 4) = (m + 4) 4c(c + 3) + 7(c + 3) = (c + 3)</p> Signup and view all the answers

Breaking an expression into factors that multiply to the original expression.

The highest value or expression shared by all terms in an expression.

A method of factorization where the GCF is factored out from the expression.

Verifying factorization by expanding the expression to see if it matches the original.

A factorization method used for expressions with four terms by grouping into pairs.

A shared binomial factor found in both groups after applying the grouping method.

The process of factoring out the GCF from each group after pairing terms in an expression.

Factoring 6x + 9 as 3(2x + 3) using the GCF of 3.

Organizing terms in an expression into groups to simplify factoring.

Extracting a common factor from grouped terms to simplify an expression further.

A factoring method for expressions in the form a² - b² = (a - b)(a + b).

Numbers that are the square of an integer, e.g., 1, 4, 9, 16.

An expression in the form ax² + bx + c where a, b, and c are constants.

Identify two numbers that multiply to ac and add to b in a quadratic.

Rewriting and simplifying a trinomial into a product of two binomials.