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Simplify By Using The Distributive Property

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Algebra

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Simplify by using the distributive property

1. (2x + 1)(x - 6)

Solution:

distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd

a = 2x, b =1, c = x, d = -6

= 2x • x + 2x ( - 6) + 1 • x + 1 • (-6)

apply minus- plus rules: +(-a ) = - a

= 2xx - 2x • 6 + 1 • x -1 • 6

= 2x

2

- 11x - 6

2. (2y - 3)(y + 2)

Solution:

distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd

a = 2y, b =-3, c = y, d = 2

= 2y • y + 2y • 2 - 3 • y - 3 • 2

= 2yy + 2y • 2 -3 y - 3 • 2

= 2y

2

+y - 6

3. (5y - 2)(3y - 1)

Solution:

distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd

a = 5y, b =-2, c = 3y, d = -1

= 5y • 3y + 5y (-1) -2 • 3y - 2 (-1)

apply minus- plus rules: - (-a ) = -a

= 5y • 3y - 5y • 1 -2 • 3y + 2 • 1

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= 15y

2

- 11y + 2

4. (5z + 1)(5z -1)

Solution:

distribute parenthesis using : (a + b) (a - b)= a

2

- b

2

a =5z, b =1

= (5x)

2

- 1

2

= 25z

2

- 1

5. (2x + 3)(2x + 3)

Solution:

apply exponent rule: a

b •

a

c

= a

b+c

(2x + 3)(2x + 3) = (2x + 3)

1+1

= (2x + 3)

2

6. (x + y)(x + y)

Solution:

apply exponent rule: a

b •

a

c

= a

b+c

(x + y)(x + y) = (x + y)

1 + 1

= (x + y)

2

7. (a - b)(a - b)

Solution:

apply exponent rule: a

b •

a

c

= a

b+c

(a - b)(a - b) = (a - b)

1 + 1

= (a - b)

2

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Simplify by using the distributive property 1. (2x + 1)(x - 6) Solution: distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd a = 2x, b =1, c = x, d = -6 = 2x • x + 2x ( - 6) + 1 • x + 1 • (-6) apply minus- plus rules: +(-a ) = - a = 2xx - 2x • 6 + 1 • x -1 • 6 = 2x2 - 11x - 6 2. (2y - 3)(y + 2) Solution: distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd a = 2y, b =-3, c = y, d = 2 = 2y • y + 2y • 2 - 3 • y - 3 • 2 = 2yy + 2y • 2 -3 y - 3 • 2 = 2y2 +y - 6 3. (5y - 2)(3y - 1) Solution: distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd a = 5y, b =-2, c = 3y, d = -1 = 5y • 3y + 5y (-1) -2 • 3y - 2 (-1) apply minus- plus rules: - (-a ) = -a = 5y • 3y - 5y • 1 -2 • 3y + 2 • 1 = 15y2 - 11y + 2 4. (5z + 1)(5z -1) Solution: distribute parenthesis using : (a + b) (a - b)= a2- b2 a =5z, b =1 = (5x)2 - 12 = 25z2 - 1 5. (2x + 3)(2x + 3) Solution: apply exponent rule: ab • ac = ab+c (2x + 3)(2x + 3) = (2x + 3)1+1 = (2x + 3)2 6. (x + y)(x + y) Solution: apply exponent rule: ab • ac = ab+c (x + y)(x + y) = (x + y)1 + 1 = (x + y)2 7. (a - b)(a - b) Solution: apply exponent rule: ab • ac = ab+c (a - b)(a - b) = (a - b)1 + 1 = (a - b)2 8. (a + b)(a + b) Solution: apply exponent rule: ab • ac = ab+c (a + b)(a + b) = (a + b)1 + 1 =(a + b)2 9. (a + 2b)(a + 3b) Solution: distribute parenthesis using : (a + b) (c + d) = ac + ad + bc + bd a = a, b =2b, c = a, d = 3b = a • a + a • 3b + 2b • a + ...
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