Solve (x+5)(x+3)^2

Question

Simplify the expression

x^{3} + 11 x^{2} + 39 x + 45

Evaluate

(x + 5) (x + 3)^{2}

Expand the expression

More Steps

Evaluate

(x + 3)^{2}

Use (a + b)^{2} = a^{2} + 2 ab + b^{2} to expand the expression

x^{2} + 2 x \times 3 + 3^{2}

Calculate

x^{2} + 6 x + 9

(x + 5) (x^{2} + 6 x + 9)

Apply the distributive property

x \times x^{2} + x \times 6 x + x \times 9 + 5 x^{2} + 5 \times 6 x + 5 \times 9

Multiply the terms

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Evaluate

x \times x^{2}

Use the product rule a^{n} \times a^{m} = a^{n + m} to simplify the expression

x^{1 + 2}

Add the numbers

x^{3}

x^{3} + x \times 6 x + x \times 9 + 5 x^{2} + 5 \times 6 x + 5 \times 9

Multiply the terms

More Steps

Evaluate

x \times 6 x

Use the commutative property to reorder the terms

6 x \times x

Multiply the terms

6 x^{2}

x^{3} + 6 x^{2} + x \times 9 + 5 x^{2} + 5 \times 6 x + 5 \times 9

Use the commutative property to reorder the terms

x^{3} + 6 x^{2} + 9 x + 5 x^{2} + 5 \times 6 x + 5 \times 9

Multiply the numbers

x^{3} + 6 x^{2} + 9 x + 5 x^{2} + 30 x + 5 \times 9

Multiply the numbers

x^{3} + 6 x^{2} + 9 x + 5 x^{2} + 30 x + 45

Add the terms

More Steps

Evaluate

6 x^{2} + 5 x^{2}

Collect like terms by calculating the sum or difference of their coefficients

(6 + 5) x^{2}

Add the numbers

11 x^{2}

x^{3} + 11 x^{2} + 9 x + 30 x + 45

Solution

More Steps

Evaluate

9 x + 30 x

Collect like terms by calculating the sum or difference of their coefficients

(9 + 30) x

Add the numbers

39 x

x^{3} + 11 x^{2} + 39 x + 45

Show Solution

x_{1} = - 5, x_{2} = - 3

Evaluate

(x + 5) (x + 3)^{2}

To find the roots of the expression,set the expression equal to 0

(x + 5) (x + 3)^{2} = 0

Separate the equation into 2 possible cases

x + 5 = 0 (x + 3)^{2} = 0

Solve the equation

More Steps

Evaluate

x + 5 = 0

Move the constant to the right-hand side and change its sign

x = 0 - 5

Removing 0 doesn't change the value,so remove it from the expression

x = - 5

x = - 5 (x + 3)^{2} = 0

Solve the equation

More Steps

Evaluate

(x + 3)^{2} = 0

The only way a power can be 0 is when the base equals 0

x + 3 = 0

Move the constant to the right-hand side and change its sign

x = 0 - 3

Removing 0 doesn't change the value,so remove it from the expression

x = - 3

x = - 5 x = - 3

Solution

x_{1} = - 5, x_{2} = - 3

Show Solution