Algebra Study Guide

Multiplying out brackets, also known as expanding expressions, means removing the brackets by multiplying each term inside the bracket by the term(s) outside. This is a fundamental skill in algebra.

When you see an expression like $a(b+c)$, it means you need to multiply $a$ by $b$ AND $a$ by $c$. So, $a(b+c) = ab + ac$. The 'a' term distributes over both terms inside the bracket.

For example, to multiply out $3(x+5)$:

1. Multiply $3 \times x$, which gives $3x$.
2. Multiply $3 \times 5$, which gives $15$.
3. Combine these results: $3x + 15$. So, $3(x+5) = 3x + 15$.

It works the same way if there's a subtraction: $2(y-4)$.

1. Multiply $2 \times y$, which gives $2y$.
2. Multiply $2 \times (-4)$, which gives $-8$.
3. Combine these results: $2y - 8$. So, $2(y-4) = 2y - 8$.

Be very careful with negative signs outside the bracket. For instance, $-(x+7)$ is the same as $-1(x+7)$.

1. Multiply $-1 \times x$, which gives $-x$.
2. Multiply $-1 \times 7$, which gives $-7$.
3. Combine: $-x - 7$. So, $-(x+7) = -x - 7$.

Similarly, $-2(3x-1)$:

1. Multiply $-2 \times 3x$, which gives $-6x$.
2. Multiply $-2 \times (-1)$, which gives $+2$ (a negative times a negative is a positive).
3. Combine: $-6x + 2$. So, $-2(3x-1) = -6x + 2$.

When multiplying out two brackets, like $(x+a)(x+b)$, you need to multiply each term in the first bracket by each term in the second bracket. A common method to remember this is FOIL for Binomials: First, Outer, Inner, Last.

For example, $(x+2)(x+3)$:

1. First: $x \times x = x^2$.
2. Outer: $x \times 3 = 3x$.
3. Inner: $2 \times x = 2x$.
4. Last: $2 \times 3 = 6$.
5. Add all these terms together: $x^2 + 3x + 2x + 6$. Then simplify by collecting like terms: $x^2 + 5x + 6$. So, $(x+2)(x+3) = x^2 + 5x + 6$.

Remember to pay close attention to signs and combine like terms after multiplying out all parts of the expression.

Multiplying out brackets, also known as expanding brackets, is a fundamental algebraic skill. It involves removing the parentheses from an expression by multiplying the term(s) outside the bracket by every term inside the bracket. For a single bracket like a(b + c), you multiply 'a' by 'b' and 'a' by 'c', then add the results: a(b + c) = ab + ac. Remember to pay close attention to the signs of the terms. If you have a negative sign outside the bracket, for example -2(x - 3), you multiply -2 by x (giving -2x) and -2 by -3 (giving +6). The result is -2x + 6. This process is essential for simplifying expressions, solving equations, and working with more complex algebraic manipulations. It is based on the distributive property of multiplication.