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Holt CA Course 1
12-6 Multiplying Binomials
Warm UpWarm Up
California StandardsCalifornia Standards
Lesson PresentationLesson Presentation
PreviewPreview
Holt CA Course 1
12-6 Multiplying Binomials
Warm UpMultiply.
1. x(x + 2)
2. –3(p – 4)
3. 2x(3x – 7)
4. Find the area of a rectangle with length
16 cm and width 21 cm.
x2 + 2x
–3p + 12
6x2 – 14x
336 cm2
Holt CA Course 1
12-6 Multiplying Binomials
Preview of Algebra 1 10.0 Students add, subtract, multiply, and divide monomials, and polynomials. Students solve multistep problems, including word problems, by using these techniques.
California Standards
Holt CA Course 1
12-6 Multiplying Binomials
Vocabulary
FOIL
Holt CA Course 1
12-6 Multiplying Binomials
You can use the Distributive Property to multiplytwo binomials.
(x + y)(x + z) = x(x + z) + y(x + z) =
x2 + xz + xy + yz
Holt CA Course 1
12-6 Multiplying Binomials
The product can be simplified using the FOIL method: multiply the First terms, the Outer terms, the Inner terms, and the Last terms of the binomials.
2First Last
Inner
Outer
Holt CA Course 1
12-6 Multiplying Binomials
Multiply.
Additional Example 1: Multiplying Two Binomials
A. (n – 2)(m – 8) B. (x + 3)(x + z)
(n – 2)(m – 8) (x + 3)(x + z)
mn – 8n – 2m + 16 x2 + xz + 3x + 3z
FOIL
Holt CA Course 1
12-6 Multiplying Binomials
Additional Example 1: Multiplying Two Binomials
Multiply.
C. (a + 3)(a + 5) D. (x – 4y)(x + 7y)
(a + 3)(a + 5) (x – 4y)(x + 7y)
a2 + 5a + 3a + 15 x2 + 7xy – 4xy – 28y2
FOIL
a2 + 8a + 15 x2 + 3xy – 28y2Combine like terms.
Holt CA Course 1
12-6 Multiplying Binomials
When you multiply two binomials, you will always get four products. Then combine like terms.
Helpful Hint
Holt CA Course 1
12-6 Multiplying Binomials
Check It Out! Example 1
Multiply.
A. (r – 4)(s – 6) B. (y + 2)(y + r)
(r – 4)(s – 6) (y + 2)(y + r)
rs – 6r – 4s + 24 y2 + ry + 2y + 2r
FOIL
Holt CA Course 1
12-6 Multiplying Binomials
Check It Out! Example 1
Multiply.
C. (a + 3)(a + 4) D. (x – 3y)(x + 8y)
(a + 3)(a + 4) (x – 3y)(x + 8y)
a2 + 4a + 3a + 12 x2 + 8xy – 3xy – 24y2
FOIL
a2 + 7a + 12 x2 + 5xy – 24y2Combine like terms.
Holt CA Course 1
12-6 Multiplying Binomials
Area of the frame = Total Area – Area of Photo
A = (8 + 2x)(10 + 2x)
= 80 + 16x + 20x + 4x2
= 36x + 4x2
An 8 in. by 10 in. photo has a wooden frame that extends x in. beyond each side. Represent the area of the frame in terms of x.
Additional Example 2
The photo area is 36x + 4x2 in2.
Total Area Area of Photo
– (8)(10)
– 80
Holt CA Course 1
12-6 Multiplying BinomialsCheck It Out! Example 2
Find the area of the border around a computer monitor of width x centimeters around a 50 cm by 80 cm screen. Represent the area of the border in terms of x.
Total Area
A = (80 + 2x)(50 + 2x)
= 4000 + 160x + 100x + 4x2
= 260x + 4x2
The border area is 260x + 4x2 cm2.
Area of border = Total Area – Area of Screen
Area of Screen
– (50)(80)
– 4000
Holt CA Course 1
12-6 Multiplying Binomials
Binomial products of the form (a + b)2, (a – b)2, and (a + b)(a – b) are often called special products.
Holt CA Course 1
12-6 Multiplying Binomials
Multiply.
Additional Example 3: Special Products of Binomials
A. (x + 6)2
(x + 6)2
(x + 6)(x + 6)
x2 + 6x + 6x + 36
x2 + 12x + 36
B. (n – m)2
(n – m)2
(n – m)(n – m)
n2 – nm – nm + m2
n2 – 2nm + m2
Holt CA Course 1
12-6 Multiplying Binomials
Additional Example 3: Special Products of Binomials
C. (x – 7)(x + 7)
(x – 7)(x + 7)
Multiply.
x2 + 7x – 7x – 49
x2 – 49 7x – 7x = 0
Holt CA Course 1
12-6 Multiplying Binomials
Check It Out! Example 3
Multiply.
A. (x + y)2
(x + y)2
(x + y)(x + y)
x2 + xy + xy + y2
x2 + 2xy + y2
B. (r – 3)2
(r – 3)2
(r – 3)(r – 3)
r2 – 3r – 3r + 9
r2 – 6r + 9
Holt CA Course 1
12-6 Multiplying Binomials
Check It Out! Example 3
C. (x – y)(x + y)
(x – y)(x + y)
Multiply.
x2 + xy – xy – y2
x2 – y2xy – xy = 0
Holt CA Course 1
12-6 Multiplying Binomials
Holt CA Course 1
12-6 Multiplying BinomialsLesson QuizMultiply.
1. (x + 5)(x + 2)
2. (c – 4)(c – 2)
3. (2y + 2)(y – 3)
4. (2m + 2)(3n + 2)
c2 – 6c + 8
2y2 – 4y – 6
6mn + 4m + 6n + 4
x2 + 7x + 10
5. (a – 1)2
6. (b + 3)(b – 3)
7. Find the area of a cement walkway of width w yd
that is around a 20 yd by 30 yd pool.
b2 – 9
a2 – 2a + 1
4w2 + 100w yd2