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iGCSE (2021 Edition)

5.02 Expansion


Expansion takes an expression from factored form and uses the distributive property to remove the brackets and write the expression as a sum of products. Such as $\left(a+2\right)\left(b+3\right)=ab+3a+2b+6$(a+2)(b+3)=ab+3a+2b+6.

The distributive property: $A\left(B+C\right)=AB+AC$A(B+C)=AB+AC

This can be used over more terms:


Or applied multiple times:

$\left(A+B\right)\left(C+D\right)$(A+B)(C+D) $=$= $A\left(C+D\right)+B\left(C+D\right)$A(C+D)+B(C+D)

You can reduce this working to one line by remembering the first term multiplies each in the second bracket, then the second term multiplies each in the second bracket.

Hence, $\left(x+5\right)\left(x+2\right)=x^2+2x+5x+10$(x+5)(x+2)=x2+2x+5x+10. Which we could then simplify to $x^2+7x+10$x2+7x+10.



After expanding check if the expression can be simplified by collecting like-terms.


Practice questions

Question 1

Expand and simplify the following:


Question 2

Expand and simplify the following expression $\left(x+7\right)\left(x-7\right)-\left(x-3\right)^2$(x+7)(x7)(x3)2

Further expansion

When multiplying more than two expressions reduce the problem to multiply two at a time.

Practice questions

Question 3

Expand the following:


Question 4

Expand $\left(3c+2\right)\left(2c^2+2\right)^2$(3c+2)(2c2+2)2.

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