To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3 ( m + 7 ) , multiply both and 7 by 3, so: 3 ( m + 7 ) = 3 × m + 3 × 7 = 3 m + 21 .

What is the formula for expanding?

To expand a bracket means to multiply each term in the bracket by the expression outside the bracket. For example, in the expression 3 ( m + 7 ) , multiply both and 7 by 3, so: 3 ( m + 7 ) = 3 × m + 3 × 7 = 3 m + 21 .

How do you expand your ab 8?

The coefficients will correspond with line n+1 of the triangle. For (a+b)8 ( a + b ) 8 , n=8 so the coefficients of the expansion will correspond with line 9 . The expansion follows the rule (a+b)n=c0anb0+c1an−1b1+cn−1a1bn−1+cna0bn ( a + b ) n = c 0 a n b 0 + c 1 a n – 1 b 1 + c n – 1 a 1 b n – 1 + c n a 0 b n .

How do you expand and simplify expressions?

In order to expand and simplify an expression, we need to multiply out the brackets and then simplify the resulting expression by collecting the like terms. Expanding brackets (or multiplying out) is the process by which we remove brackets.

How do you write a number in expanded form?

Writing the number in expanded form means to write the value of each digit then add them together to find the sum. For example, the number 1,234 has the following values: The value of 1 is written as 1,000 because it’s in the thousands place. The value of 2 is written as 200 because it’s in the hundreds place.

How do you expand a binomial expression using Pascal’s triangle?

Binomial Expansions Using Pascal’s Triangle

1. There is one more term than the power of the exponent, n.
2. In each term, the sum of the exponents is n, the power to which the binomial is raised.
3. The exponents of a start with n, the power of the binomial, and decrease to 0.

What is the expansion of a B 6?

The coefficients will correspond with line n+1 of the triangle. For (a+b)6 ( a + b ) 6 , n=6 so the coefficients of the expansion will correspond with line 7 . The expansion follows the rule (a+b)n=c0anb0+c1an−1b1+cn−1a1bn−1+cna0bn ( a + b ) n = c 0 a n b 0 + c 1 a n – 1 b 1 + c n – 1 a 1 b n – 1 + c n a 0 b n .

What is Pascal’s triangle formula?

Solution: Using the Pascals triangle formula for the sum of the elements in the nth row of the Pascals triangle: Sum = 2n where n is the number of the row.

What does expanding a expression mean?

Expanding Algebraic Expressions. When we expand an algebraic expression, we combine more than one number or variable by performing the given algebraic operation(s). We do this by using the distributive property to remove any parentheses or brackets and by combining like terms.

How do you write binomial expansion?

The binomial theorem formula is used in the expansion of any power of a binomial in the form of a series. The binomial theorem formula is (a+b)n= ∑nr=0nCr an-rbr, where n is a positive integer and a, b are real numbers, and 0 < r ≤ n.

What is the expansion of X Y n?

For any positive integer n, the expansion of (x + y)n is C(n, 0)xn + C(n, 1)xn-1y + C(n, 2)xn-2y2 + + C(n, n – 1)xyn-1 + C(n, n)yn. Each term r in the expansion of (x + y)n is given by C(n, r – 1)xn-(r-1)yr-1. Example: Write out the expansion of (x + y)7.