Expand Perfect Squares
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Question 1 of 7
1. Question
Expand and simplify.`(x+5)^2`Hint
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Incorrect
Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$`(x+5)^2``a=x``b=5`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{x}+\color{#9a00c7}{5})^2$$ `=` $$\color{#00880A}{x}^2+2(\color{#00880A}{x})(\color{#9a00c7}{5})+\color{#9a00c7}{5}^2$$ `=` `x^2+10x+25` Simplify `x^2+10x+25` -
Question 2 of 7
2. Question
Expand and simplify.`(3m+2)^2`Hint
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Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$`(3m+2)^2``a=3m``b=2`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{3m}+\color{#9a00c7}{2})^2$$ `=` $$\color{#00880A}{3m}^2+2(\color{#00880A}{3m})(\color{#9a00c7}{2})+\color{#9a00c7}{2}^2$$ `=` `9m^2+12m+4` Simplify `9m^2+12m+4` -
Question 3 of 7
3. Question
Expand and simplify.`(ab-4c)^2`Hint
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Correct!
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Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$$`(ab-4c)^2``a=ab``b=4c`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{ab}-\color{#9a00c7}{4c})^2$$ `=` $$(\color{#00880A}{ab})^2-2(\color{#00880A}{ab})(\color{#9a00c7}{4c})+(\color{#9a00c7}{4c})^2$$ `=` `a^2 b^2-8abc+16c^2` Simplify `a^2 b^2-8abc+16c^2` -
Question 4 of 7
4. Question
Expand and simplify.`(2t+9)^2`Hint
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Great Work!
Incorrect
Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$`(2t+9)^2``a=2t``b=9`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{2t}+\color{#9a00c7}{9})^2$$ `=` $$\color{#00880A}{2t}^2+2(\color{#00880A}{2t})(\color{#9a00c7}{9})+\color{#9a00c7}{9}^2$$ `=` `4t^2+36t+81` Simplify `4t^2+36t+81` -
Question 5 of 7
5. Question
Expand and simplify.`(6a-5)^2`Hint
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Keep Going!
Incorrect
Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$$`(6a-5)^2``a=6a``b=5`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$(\color{#00880A}{6a}-\color{#9a00c7}{5})^2$$ `=` $$(\color{#00880A}{6a})^2-2(\color{#00880A}{6a})(\color{#9a00c7}{5})+(\color{#9a00c7}{5})^2$$ `=` `36a^2-60a+25` Simplify `36a^2-60a+25` -
Question 6 of 7
6. Question
Expand and simplify.`(a+1/4)^2`Hint
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Excellent!
Incorrect
Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$`(a+1/4)^2``a=a``b=1/4`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$\left(\color{#00880A}{a}+\color{#9a00c7}{\frac{1}{4}}\right)^2$$ `=` $$\color{#00880A}{a}^2+2(\color{#00880A}{a})\left(\color{#9a00c7}{\frac{1}{4}}\right)+\color{#9a00c7}{\frac{1}{4}}^2$$ `=` `a^2+a/2+1/((4)^2)` Simplify `=` `a^2+a/2+1/(16)` Simplify `a^2+a/2+1/(16)` -
Question 7 of 7
7. Question
Expand and simplify.`(2y-3/y)^2`Hint
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Well Done!
Incorrect
Expanding Perfect Square Binomials
$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2=\color{#00880A}{a}^2+2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2=\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$First, label the values in the given expression.$$(\color{#00880A}{a}+\color{#9a00c7}{b})^2$$`(2y-3/y)^2``a=2y``b=3/y`Substitute the values into the formula given for Expanding Perfect Square Binomials.$$(\color{#00880A}{a}-\color{#9a00c7}{b})^2$$ `=` $$\color{#00880A}{a}^2-2\color{#00880A}{a}\color{#9a00c7}{b}+\color{#9a00c7}{b}^2$$ $$\left(\color{#00880A}{2y}-\color{#9a00c7}{\frac{3}{y}}\right)^2$$ `=` $$\color{#00880A}{2y}^2-2(\color{#00880A}{2y})\left(\color{#9a00c7}{\frac{3}{y}}\right)+\color{#9a00c7}{\frac{3}{y}}^2$$ `=` `4y^2-2(2times3)+((3)^2)/((y)^2)` `ytimes1/y` cancels out` `=` `4y^2-12+9/(y^2)` Simplify `4y^2-12+9/(y^2)`
Quizzes
- Binomial Products – Distributive Property
- Binomial Products – FOIL Method
- FOIL Method – Same First Variable 1
- FOIL Method – Same First Variable 2
- FOIL Method – 3 Terms
- Expand Perfect Squares
- Difference of Two Squares
- Expand Longer Expressions
- Highest Common Factor 1
- Highest Common Factor 2
- Factorise a Polynomial (HCF)
- Factorise a Polynomial 1
- Factorise a Polynomial 2
- Factorise a Polynomial with Integers
- Factorise Difference of Two Squares 1
- Factorise Difference of Two Squares 2
- Factorise Difference of Two Squares 3
- Factorise by Grouping in Pairs
- Factorise Difference of Two Squares (Harder) 1
- Factorise Difference of Two Squares (Harder) 2
- Factorise Difference of Two Squares (Harder) 3
- Factorise Trinomials (Quadratics) 1
- Factorise Trinomials (Quadratics) 2
- Factorise Trinomials (Quadratics) 3
- Factorise Trinomials (Quadratics) w Coefficient more than 1 (1)
- Factorise Trinomials (Quadratics) w Coefficient more than 1 (2)
- Factorise Trinomials (Quadratics) w Coefficient more than 1 (3)
- Factorise Trinomials (Quadratics) – Complex