Solve (x + 3) ^ 2 - 2(x ^ 2 + 3x - 1) | Equatix - Math Solver

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Example

3(r+2s)=2t-4

a⋅(b-2)=3b

3(r+2s)=2t-4

a⋅(b-2)=3b

Question

$$(x+3)^{2}-2(x^{2}+3x-1)$$

Evaluate

$11-x^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+3\right)^{2}$.

$$x^{2}+6x+9-2\left(x^{2}+3x-1\right)$$

Use the distributive property to multiply $-2$ by $x^{2}+3x-1$.

$$x^{2}+6x+9-2x^{2}-6x+2$$

Combine $x^{2}$ and $-2x^{2}$ to get $-x^{2}$.

$$-x^{2}+6x+9-6x+2$$

Combine $6x$ and $-6x$ to get $0$.

$$-x^{2}+9+2$$

Add $9$ and $2$ to get $11$.

$$-x^{2}+11$$

Expand

$11-x^{2}$

Solution Steps

Use binomial theorem $\left(a+b\right)^{2}=a^{2}+2ab+b^{2}$ to expand $\left(x+3\right)^{2}$.

$$x^{2}+6x+9-2\left(x^{2}+3x-1\right)$$

Use the distributive property to multiply $-2$ by $x^{2}+3x-1$.

$$x^{2}+6x+9-2x^{2}-6x+2$$

Combine $x^{2}$ and $-2x^{2}$ to get $-x^{2}$.

$$-x^{2}+6x+9-6x+2$$

Combine $6x$ and $-6x$ to get $0$.

$$-x^{2}+9+2$$

Add $9$ and $2$ to get $11$.

$$-x^{2}+11$$