Solve (1-x)(1+x)-2(1+x)-3(1+x) | 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

$$(1-x)(1+x)-2(1+x)-3(1+x)$$

Evaluate

$-\left(x+1\right)\left(x+4\right)$

Solution Steps

Consider $\left(1-x\right)\left(1+x\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

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

Calculate $1$ to the power of $2$ and get $1$.

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

Use the distributive property to multiply $-2$ by $1+x$.

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

Subtract $2$ from $1$ to get $-1$.

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

Use the distributive property to multiply $-3$ by $1+x$.

$$-1-x^{2}-2x-3-3x$$

Subtract $3$ from $-1$ to get $-4$.

$$-4-x^{2}-2x-3x$$

Combine $-2x$ and $-3x$ to get $-5x$.

$$-4-x^{2}-5x$$

Expand

$-x^{2}-5x-4$

Solution Steps

Consider $\left(1-x\right)\left(1+x\right)$. Multiplication can be transformed into difference of squares using the rule: $\left(a-b\right)\left(a+b\right)=a^{2}-b^{2}$.

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

Calculate $1$ to the power of $2$ and get $1$.

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

Use the distributive property to multiply $-2$ by $1+x$.

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

Subtract $2$ from $1$ to get $-1$.

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

Use the distributive property to multiply $-3$ by $1+x$.

$$-1-x^{2}-2x-3-3x$$

Subtract $3$ from $-1$ to get $-4$.

$$-4-x^{2}-2x-3x$$

Combine $-2x$ and $-3x$ to get $-5x$.

$$-4-x^{2}-5x$$