The key thing to remember about multiplying brackets is that the thing outside the brackets multiplies each separate term inside the brackets.
Example 1
Expand the following:
9) 3(2x + 5)
= 3 * 2x = 6x
= 3 * 5 = 15
Answer: 6x + 15
c) 2e le-4)
z2exez 2e²
= 2ex - 4 = -8e
Answer = 2e² - 8e
Example 2
b) -4(3y-2)
= -4 * 3y = -12y
-4 * -2 = 8
Expand x(2x+1) + y(y=4) + 3x(yt 2)
= x * 2x + x * 1 + 3x * y + 3x * 2
= 2x² + x + 6x + 3xy + y² - 44
= 2x² + 7x + 3xy + y² - 49
Answer: -12y + 8
Expanding Double Brackets
Using the FOIL method to multiply out double brackets:
First - Multiply the first term in each bracket together.
Outside - Multiply the outside terms (i.e. the first term in the first bracket by the second term in the second bracket).
Inside - Multiply the inside terms (i.e. the second term in the first bracket by the first term in the second bracket).
Last - Multiply the second term in each bracket together.
When multiplying double brackets, you get 4 terms and 2 of them usually combine to leave 3 terms.
Example 1
Expand and simplify (x+3)(x+8)
= (xx) + (x8) + (3x) + (38)
= x² + 11x + 24
Example 2
Expand and simplify (2)(2n+7)
= (2n) + (27) + (-2n) + (-27)
= 2n² + 14 - 2n - 14
= 2n² - 2n
Writing Out Squared Brackets as Double Brackets
Always write out squared brackets as double brackets.
Example 3
Expand and Simplify (3x+2)²
= (3x+2)(3x+2)
= 9x² + 6x + 6x + 4
= 9x² + 12x + 4
