Factoring Trinomials by Grouping

Factoring by Grouping

ac + ad + bc + bd = (a + b)(c + d)

Grouping means isolating terms using parenthesis( )

• Example: ab + ac + mb + mc can be grouped into:

• (ab + ac) + (mb + mc)

• What is common to the first group? a

• What is common to the second group? m

• Hence, we can factor them in this manner: a(b + c) + m(b + c)

• What is common to both groups? (b + c)

Factoring by Grouping

• EXAMPLE NO. ! Factor: ab + ac + mb + mc

• Step no.1 Group the terms. (ab + ac) + (mb + mc)

• Step 2: Get the CMF or common monomial factor in each group

• Step 3: Factor this out: a(b + c) + m(b + c)

• Step 4: Get the common binomial factor.and factor this out.

• Hence, ab + ac + mb + mc= (b + c)(a + m)

Examples:

Ex.1. Factor: 2x + 2y + ax + ay

Solution: (2x + 2y) + (ax + ay) = 2(x + y) + a(x + y)

.............................................................. = (x + y)(2 + a)

Ex. 2. Factor completely: 4ab³ - abc² + 5b² - 5c²

Solution: (4ab³ - abc² )+ (8b² - 2c²) = ab(4b²- c²) + 2(4b² - c²)

..........................................................................=(4b²- c²)(ab + 2)

......................................................................... = (2b + c)(2b - c)(ab + 2)

Multiple Choice

What is the best groupings of the terms in the polynomial:

3x + 3y + bx + by

• (3x + 3y) + (bx + by)

• (3x + 3y)(bx + by)

• (3x + by) + (3y + bx)

Multiple Choice

What monomial is common to both terms: 10mn - 10mp?

• 10

• m

• 10m

Multiple Choice

What binomial is common in the following expression?

a(5 - y) + b(5 - y)?

• (a + b)

• (5 - y)

• a(5 - y)

Multiple Choice

Factor : 9x + 9y + mx + my

• 9(x + y)

• m(x + y)

• (x + y)(9 + m)

Multiple Choice

Group the terms in this expression: 2a + 3bm + 2m + 3ab

• (2a + 2m) + (3bm + 3ab)

• (2a + 2m) + (3ab + 3bm)

• (2a + 3bm) + (2m + 3ab)

Multiple Choice

Factor completely: 2a + 3bm + 2m + 3ab

• (a + m)(2 + 3b)

• (a + 2)(m + 3b)

• a + 3b)(2 + m)

Multiple Choice

Factor: 6xy - 6xz + 7my - 7mz

• (6xy - 6xz)(7my - 7mz)

• (y - z)(6x + 7m)

• (6 - my)(7 + xz)

Multiple Choice

Factor completely: 8x³ - 2xy² + 20x² - 5y²

• (x²- y²)(2x + 5)

• (4x²- y²)(2x + 5)

• (2x + y)(2x - y)(2x + 5)

Multiple Choice

The common binomial factor in 7a(m + n) - b(m + n) is:

• 7a - b

• m + n

• m - n

Multiple Choice

The common binomial factor in 3ax - 3ay + bx - by is:

• x - y

• x + y

• 3a + b

• 3a - b

Congratulations!

• Study well!

• Keep on going....