Multiplying out Quadratics

6 Multiplying out Quadratics

(x + 1)(x + 2) 100 0

x2 + 3x + 2 Well done, both brackets have the same sign so the inner and outer terms 'add up'. 1

100

x2 + 3x + 3 Nope, multiply the outer elements; 2 x 1 is 2 0

2x + 3x + 2 Nope, x times x is x2; the power goes up by one 0

2x<sup2 + x + 3 Nope, x times x is x2 and 2 x 1 is 2 0

(x + 1)(x - 1) 100 0

x2 - 1 Yes, the terms in x disappear as they have opposite sign and the same size. This is an example of the 'difference of two squares' 1

100

x2 + 2x - 1 Nope, check the sign of the middle two terms, they should cancel out 0

x2 - 2 Nope, check the Last terms, the constants. -1 times 1 is -1, not -2 0

2x - 2 Nope, x times x is always x2 0

(x + 4)(x - 4) 100 0

x2 - 16 Yes, the terms in x disappear as they have opposite sign and same size. This is an example of the 'difference of two squares' 1

100

x2 + 8x - 16 Nope, check the sign of the middle two terms, they should cancel out 0

x2 - 8 Nope, check the Last terms, the constants. -4 times 4 is -16, not -8 0

2x - 16 Nope, x times x is always x2 0

(x + 5)(x + 2) 100 0

x2 + 7x + 10 Well done, the brackets have the same sign, so the outer and inner terms add to give 7x 1

100

x2 + 3x + 10 Nope, +5x and +2x makes 7x 0

x2 + 7x + 7 Nope, the constants or Outer terms are multiplied, so 5 x 2 = 10 0

x + 7x + 10 Nope, x times x is x2 0

(x + 5)2 100 0

x2 + 10x + 25 Yup, just write the bracket times the bracket and multiply out using FOIL as usual. 1

100

x2 + 25 Nope, write (x + 5)(x + 5) and then multiply out using FOIL. The x terms don't cancel. 0

x2 + 10x + 10 Nope, 5 x 5 is 25, not 10. The x terms add, but the constants multiply 0

2x + 10x + 25 Nope, x times x is always x2 0

(x + 2)(x - 3) 100 0

x2 - x -6 Yup, brackets have opposite signs, so the outer and inner 'subtract' and the negative term is the largest 1

100

x2 + x -6 Nope, the outer comes to -3x and the inner comes to +2x, so you end up owing an x 0

x2 - x -5 Nope, +2 times -3 is -6, not -5. Check multiplying directed numbers. 0

x2 +5x -6 Nope, the outer comes to -3x and the inner comes to +2x, so you end up owing an x. You must check your directed numbers. 0

(x - 2)(x + 3) 100 0

x2 + x -6 Yup! The outer term gives +3x and the inner term gives -2x so you end up with +1x. 1

100

x2 - x -6 Nope, Outer term gives +3x and inner term gives -2x, so you come out positive 0

x2 + 5x -6 Nope, the signs of the x terms (inner and outer) are different, so you subtract 3 and 2. 0

x2 - 5x -6 Nope, the signs of the x terms (inner and outer) are different, so you subtract 3 and 2. 0

(x - 4)(x - 2) 100 0

x2 - 6x + 8 Yup, inner and outer terms have the same sign so x's get 'more negative'. -4 times -2 is +8 1

100

x2 + 6x + 8 Nope, both inner and outer terms are negative, so you end up with -6x 0

x2 - 6x - 6 Nope, last term is -4 times -2, and minus times a minus is a positive number. 2 times 4 is 8! 0

x2 - 6x - 8 Nope, last term is -4 times -2, and minus times a minus is a positive number 0

(x + 10)(x - 1) 100 0

x2 + 9x - 10 Yup! Brackets have opposite sign so the last term is negative, and the outer and inner terms 'subtract' and take the sign of the largest number. 1

100

x2 + 11x - 10 Nope, check the inner and outer terms. 0

x2 - 9x - 10 Nope, check the inner and outer terms, is the + term larger? 0

x2 + 9x - 9 Nope, what is +10 times -1 0

x(x - 1) 100 0

x2 - x Yup, just multiply through by x 1

100

x2 - 1 Nope, x times -1 is -x 0

x2 + x Nope, + times - is - 0

x + 1 Nope, x times x is x2 0

(2x + 3)(4x + 2) 100 0

8x2 +16x +6 Yup, inner gives 12x and outer gives 4x and these add 1

100

6x2 +16x +6 Nope, 2x times 4x is 8x2, you have to multiply the numbers and the letters in the first term 0

8x2 +16x +5 Nope, the last term needs checking! 0

8x2 +12x +6 Nope, the inner term gives 12x on its own. What about the outer term? 0

(2x + 2)(x - 1) 100 0

2x2 - 2 Yup, by coincidence, the outer term and the inner term cancel each other out leaving just the first and last. 1

100

2x2 - 4x - 2 Nope, the outer term gives 2x times -1 and the inner term gives +2 times +x. What happens when you add these terms? 0

2x2 + 4x - 2 Nope, the outer term gives 2x times -1 and the inner term gives +2 times +x. What happens when you add these terms? 0

2x2 + 2 Nope, what is the sign of +2 times -1 0

(3x + 4)(x - 4) 100 0

3x2 - 8x - 16 Yup, the constant term in each bracket have opposite signs so take the difference of the x terms 1

100

3x2 - 16 Nope, the inner and outer terms don't cancel. Check them again. 0

3x2 + 8x - 16 Nope, outer is -12x and inner is +4x, how many x do you get when you collect these like terms? 0

3x2 - 8x Nope, you multiply the -4 and +4, not add them! 0

(2x + 4)(2x - 4) 100 0

4x2 - 16 Yes, the 'difference of two squares' where the x terms cancel out 1

100

4x2 +16x - 16 Nope, check the inner and outer terms again! 0

4x2 -16x - 16 Nope, check the inner and outer terms again! 0

4x2 - 8 Nope, check the last term again! 0

(5x + 1)(x - 5) 100 0

5x2 - 24x - 5 Yup, both negative because different signs in each bracket and largest constant is negative 1

100

5x2 - 26x - 5 Nope, check the signs of the outer and inner terms 0

5x2 + 24x - 5 Nope, check the signs of the outer and inner terms 0

5x2 - 24x - 4 Nope, you multiply the last two numbers, not add them! 0

(2x + 1)(4x + 3) 100 0

8x2 + 10x +3 Yup! all positive and the inner and outer terms add 1

100

6x2 + 10x +3 Nope, check the first term, multiply the numbers 0

8x2 + 10x +4 Nope, check the last term 0

8x + 10x +3 Nope, check the first term, x times x is x2 0

(3x - 2)(2x - 3) 100 0

6x2 -13x + 6 Yup, the brackets have the same signs so the x terms are going in the same direction, and the constants multiply to positive. 1

100

6x2 -13x - 6 Nope, check the last term! 0

6x2 +13x + 6 Nope, check the signs of the outer and inner terms 0

6x2 -5x + 6 Nope, check the signs of the outer and inner terms 0

(2x - 4)(x - 2) 100 0

2x2 - 8x + 8 Yup, brackets both negative so inner and outer numbers add with negative sign and constant is positive 1

100

2x2 + 8 Nope, check the inner and outer terms again! 0

2x2 + 8x + 8 Nope, check the inner and outer terms again! 0

2x2 - 8x + 7 Nope, check the last term again! You are multiplying... 0

(7x + 3)(4x + 2) 100 0

28x2 + 26x + 6 Yup, both brackets positive so inner and outer add, constant is positive 1

100

28x2 + 26x + 5 Nope, check last term, you are multiplying to get each term 0

11x2 + 26x + 6 Nope, check the first term, multiply both the numbers and the letters 0

28x + 26x + 6 Nope, check the first term, multiply x by x 0

(3x - 2)2 100 0

9x2 - 12x + 4 Yup, brackets same sign so outer and inner 'add up' to -12x, and constant is positive 1

100

9x2 + 4 Nope, check the outer and inner terms and the signs 0

9x2 + 12x - 4 Nope, check the signs on your terms! 0

9x2 - 12x - 4 Nope, check the sign of your last term! 0

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