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Question 1 of 5
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When factorising trinomials, use the Cross Method.
Use the cross method to factorise 21+43a+20a2
Start by drawing a cross.
Now, find two values that will multiply into 21 and write them on the left side of the cross.
7 and 3 fits this description.
Next, find two numbers that will multiply into 20a2 and, when cross-multiplied to the values to the left side, will add up to 43a.
|
Product |
Sum when Cross-Multiplied |
| 2a and 10a |
20a2 |
(3×2a)+(7×10a)=76a |
| 5a and 4a |
20a2 |
(3×5a)+(7×4a)=43a |
| 20a and 1a |
20a2 |
(3×20a)+(7×1a)=67a |
5a and 4a fits this description.
Now, write 5a and 4a on the right side of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is (7+5a)(3+4a).
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Question 2 of 5
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When factorising trinomials, use the Cross Method.
Use the cross method to factorise 56+19y-10y2
Start by drawing a cross.
Now, find two values that will multiply into 56 and write them on the left side of the cross.
7 and 8 fits this description.
Next, find two numbers that will multiply into -10y2 and, when cross-multiplied to the values to the left side, will add up to 19y.
|
Product |
Sum when Cross-Multiplied |
| -y and 10y |
-10y2 |
(8×-y)+(7×10y)=62y |
| -2y and 5y |
-10y2 |
(8×-2y)+(7×5y)=19y |
-2y and 5y fits this description.
Now, write -2y and 5y on the right side of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is (7-2y)(8+5y).
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Question 3 of 5
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When factorising trinomials, use the Cross Method.
Use the cross method to factorise x2+5xy+4y2
Start by drawing a cross.
Now, find two values that will multiply into x2 and write them on the left side of the cross.
x and x fits this description.
Next, find two numbers that will multiply into 4y2 and, when cross-multiplied to the values to the left side, will add up to 5xy.
|
Product |
Sum when Cross-Multiplied |
| 2y and 2y |
4y2 |
(x×2y)+(x×2y)=4xy |
| 4y and y |
4y2 |
(x×4y)+(x×y)=5xy |
4y and y fits this description.
Now, write 4y and y on the right side of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is (x+4y)(x+y).
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Question 4 of 5
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When factorising trinomials, use the Cross Method.
Use the cross method to factorise 6x2+xy-2y2
Start by drawing a cross.
Now, find two values that will multiply into 6x2 and write them on the left side of the cross.
Either 6x and x or 2x and 3x fits this description. Try 2x and 3x first.
Next, find two numbers that will multiply into -2y2 and, when cross-multiplied to the values to the left side, will add up to xy.
|
Product |
Sum when Cross-Multiplied |
| -2y and y |
-2y2 |
(3x×-2y)+(2x×y)=-4xy |
| -y and 2y |
-2y2 |
(3x×-y)+(2x×2y)=xy |
-y and 2y fits this description.
Now, write -y and 2y on the right side of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is (2x-y)(3x+2y).
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Question 5 of 5
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When factorising trinomials, use the Cross Method.
Use the cross method to factorise 28x2+xy-2y2
Start by drawing a cross.
Now, find two values that will multiply into -2y2 and write them on the left side of the cross.
-2y and y fits this description.
Next, find two numbers that will multiply into 28x2 and, when cross-multiplied to the values to the left side, will add up to xy.
|
Product |
Sum when Cross-Multiplied |
| 2x and 14x |
28x2 |
(2x×y)+(14x×-2y)=-26xy |
| 7x and 4x |
28x2 |
(7x×y)+(4x×-2y)=xy |
7x and 4x fits this description.
Now, write 7x and 4x on the right side of the cross.
Finally, group the values in a row with a bracket and combine the brackets.
Therefore, the factorised expression is (7x+2y)(4x-y).
