01.03 Expanding Brackets
In this lesson you will learn how to:
- Expand and simplify products of two expressions, each with multiple terms
- Expand and simplify products of three expressions, each with multiple terms
Prerequisites from previous chapters:
- N/A
VIDEO LESSON
INTERACTIVE SELF-STUDY
When multiplying two expressions, we need to multiply each term in first expression by each term in the second expression
Worked Example 1 – (GRADE E)
Expand and simplify \((5x-7)(3x-4y+2)\)
\((\color{red}{5x}\color{orange}{-7})(3x-4y+2)\)
\(=\color{red}{5x}(3x-4y+2)\color{orange}{-7}(3x-4y+2)\)
\(=15x^2-20xy+10x-21x+28y-14\)
\(=15x^2-20xy-11x+28y-14\)
Notice we have multiplied \(5x\) by every term in the second bracket
Then multiplied \(-7\) by every term in the second bracket
Finally we add everything together, grouping the like terms.
When given an expression of the form \((a+b)^2\), it means you have two copies of \((a+b)\) being multiplied.
You can therefore write the bracket down twice to help you expand it: \((a+b)^2=(a+b)(a+b)\)
i. Expand and simplify \((a+b)^2\)
- \((a+b)^2=a^2+2ab+b^2\)
Example 2 – (GRADE E)
Expand and simplify the following expressions
a. \((2x+3)(x-4)\)
c. \((5x-3y)^2\)
d. \((2x+y)(7x-4y+1)\)
PRODUCTS OF THREE EXPRESSIONS
You can also be asked to find the product of three expressions
You multiply two of the expressions together and then multiply the resulting product by the final expression.
For example to find \((a+b)(c+d)(e+f)\), you can perform \(\bigg[(a+b)(c+d)\bigg]\times (e+f)\)
Multiplication is associative. This means that the order you multiply does not matter
So we could equally perform \(\bigg[(a+b)(e+f)\bigg]\times (c+d)\) or \(\bigg[(c+d)(e+f)\bigg]\times (a+b)\) and obtain the same answer
When given an expression of the form \((a+b)^3\), it means you have three copies of \((a+b)\) being multiplied.
You can therefore write the bracket down three times to help you expand it: \((a+b)^3=(a+b)(a+b)(a+b)\)
Example 3 – (GRADE E)
Expand and simplify the following expressions
a. \(x(5x-3)(x+1)\)
c. \((x+1)(5x-1)(x+2)\)
d. \((3x-2y)^3\)
END OF LESSON!
You can now answer:
EDEXCEL Pure Year 1 Ex 1B – All Questions (Including Challenge Question*)
OCR A Student Book 1 Ex 2A – Q16