School Students    Algebra   Quadratics 
Difference of two squares     Common Factors

Quadratic answers

I will go through the first one with all the complete instructions

1. Multiply the first term in the first bracket by all the terms in the second bracket.
2. Multiply the second term in the first bracket by all the terms in the second bracket.
3. Add /subtract all these terms together. Watch out for those Minus signs!
4. Continue until the last term in the first bracket.

Example

1.  (x + 10)( x -  5)

Multiply the first term in the first bracket by all the terms in the second bracket.

(x + 10)( x -  5) = (x  x x) + (x  x (-  5)) =   x²  -  5 x   this the first step only
                       Watch out for the minus sign

Multiply the second term in the first bracket by all the terms in the second bracket.

 (x + 10)( x -  5) = x²  -  5x + (10  x x ) +  (10  x (-  5)) = x² - 5x + 10x -  50
                                 Watch out for the minus sign

Now add or subtract like terms,

 (x + 10)( x -  5) = x² -  5x + 10x -  50  =  x²  + 5x  -  50

Back to questions

2.  (x -  3)( x -  6)

Multiply the first term in the first bracket by all the terms in the second bracket.

(x - 3)( x -  6) = (x  x x) + ( x  x (-  6 )) =   x²  -  6 x   this the first step only
                       Watch out for the minus sign

Multiply the second term in the first bracket by all the terms in the second bracket.

 (x - 3)( x -  6) = x²  -  6x + ((- 3)  x x) + ((- 3)  x (- 6)) = x² - 6x - 3x +  18
                                 Watch out for the minus signs

Now add or subtract like terms,

 (x - 3)( x -  6) =  x² - 6x - 3x +  18 =  x² - 9x  +  18

Back to questions

3. (x + 2)( x -  15)

 (x + 2)( x -  15) = (x  x x) + ( x  x (-15 )) + ( 2  x x) + (( 2  x (- 15)) 
                                  Watch out for the minus signs

= x² - 15x + 2x - 30 =  x² - 13x  - 30
                               

Back to questions

Check One

    Expanding the bracket to check that the factorisation is correct.

(x + 4)( x + 3) = x² + 3x + 4x +  12 =  x² + 7x  +  12

Yes the brackets multiply out to give the same expression.

Back to quadratic explanation

Check Two

Expanding the bracket to check that the factorisation is correct.

(x + 8)( x + 4) = x² + 4x + 8x +  32 =  x² + 12x  +  32

Yes the brackets multiply out to give the same expression.

Back to quadratic explanation

Check Three

Expanding the bracket to check that the factorisation is correct.

(x + 8)( x -  3) = x² -  3x + 8x -  24=  x² + 5x - 24

Yes the brackets multiply out to give the same expression.

Back to quadratic explanation

Home

Contact me

About me

Services

Feedback

Events