Factor Quadratics (Complex)
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Question 1 of 5
1. Question
Factorise.`21+43a+20a^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `21+43a+20a^2`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 `20a^2` and, when crossmultiplied to the values to the left side, will add up to `43a`.Product Sum when CrossMultiplied `2a` and `10a` `20a^2` `(3times2a)+(7times10a)=76a` `5a` and `4a` `20a^2` `(3times5a)+(7times4a)=43a` `20a` and `1a` `20a^2` `(3times20a)+(7times1a)=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)`.`(7+5a)(3+4a)` 
Question 2 of 5
2. Question
Factorise.`56+19y10y^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `56+19y10y^2`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 `10y^2` and, when crossmultiplied to the values to the left side, will add up to `19y`.Product Sum when CrossMultiplied `y` and `10y` `10y^2` `(8timesy)+(7times10y)=62y` `2y` and `5y` `10y^2` `(8times2y)+(7times5y)=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 `(72y)(8+5y)`.`(72y)(8+5y)` 
Question 3 of 5
3. Question
Factorise.`x^2+5xy+4y^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `x^2+5xy+4y^2`Start by drawing a cross.Now, find two values that will multiply into `x^2` and write them on the left side of the cross.`x` and `x` fits this description.Next, find two numbers that will multiply into `4y^2` and, when crossmultiplied to the values to the left side, will add up to `5xy`.Product Sum when CrossMultiplied `2y` and `2y` `4y^2` `(xtimes2y)+(xtimes2y)=4xy` `4y` and `y` `4y^2` `(xtimes4y)+(xtimesy)=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)`.`(x+4y)(x+y)` 
Question 4 of 5
4. Question
Factorise.`6x^2+xy2y^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `6x^2+xy2y^2`Start by drawing a cross.Now, find two values that will multiply into `6x^2` 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 `2y^2` and, when crossmultiplied to the values to the left side, will add up to `xy`.Product Sum when CrossMultiplied `2y` and `y` `2y^2` `(3xtimes2y)+(2xtimesy)=4xy` `y` and `2y` `2y^2` `(3xtimesy)+(2xtimes2y)=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 `(2xy)(3x+2y)`.`(2xy)(3x+2y)` 
Question 5 of 5
5. Question
Factorise.`28x^2+xy2y^2`Hint
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When factorising trinomials, use the Cross Method.Use the cross method to factorise `28x^2+xy2y^2`Start by drawing a cross.Now, find two values that will multiply into `2y^2` and write them on the left side of the cross.`2y` and `y` fits this description.Next, find two numbers that will multiply into `28x^2` and, when crossmultiplied to the values to the left side, will add up to `xy`.Product Sum when CrossMultiplied `2x` and `14x` `28x^2` `(2xtimesy)+(14xtimes2y)=26xy` `7x` and `4x` `28x^2` `(7xtimesy)+(4xtimes2y)=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)(4xy)`.`(7x+2y)(4xy)`
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