Solve ((M+9)(M-5))-((M-8)(M+4)) | 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

$$((M+9)(M-5))-((M-8)(M+4))$$

Evaluate

$8M-13$

Solution Steps

Apply the distributive property by multiplying each term of $M+9$ by each term of $M-5$.

$$M^{2}-5M+9M-45-\left(M-8\right)\left(M+4\right)$$

Combine $-5M$ and $9M$ to get $4M$.

$$M^{2}+4M-45-\left(M-8\right)\left(M+4\right)$$

Apply the distributive property by multiplying each term of $M-8$ by each term of $M+4$.

$$M^{2}+4M-45-\left(M^{2}+4M-8M-32\right)$$

Combine $4M$ and $-8M$ to get $-4M$.

$$M^{2}+4M-45-\left(M^{2}-4M-32\right)$$

To find the opposite of $M^{2}-4M-32$, find the opposite of each term.

$$M^{2}+4M-45-M^{2}-\left(-4M\right)-\left(-32\right)$$

The opposite of $-4M$ is $4M$.

$$M^{2}+4M-45-M^{2}+4M-\left(-32\right)$$

The opposite of $-32$ is $32$.

$$M^{2}+4M-45-M^{2}+4M+32$$

Combine $M^{2}$ and $-M^{2}$ to get $0$.

$$4M-45+4M+32$$

Combine $4M$ and $4M$ to get $8M$.

$$8M-45+32$$

Add $-45$ and $32$ to get $-13$.

$$8M-13$$

Expand

$8M-13$

Solution Steps

Apply the distributive property by multiplying each term of $M+9$ by each term of $M-5$.

$$M^{2}-5M+9M-45-\left(M-8\right)\left(M+4\right)$$

Combine $-5M$ and $9M$ to get $4M$.

$$M^{2}+4M-45-\left(M-8\right)\left(M+4\right)$$

Apply the distributive property by multiplying each term of $M-8$ by each term of $M+4$.

$$M^{2}+4M-45-\left(M^{2}+4M-8M-32\right)$$

Combine $4M$ and $-8M$ to get $-4M$.

$$M^{2}+4M-45-\left(M^{2}-4M-32\right)$$

To find the opposite of $M^{2}-4M-32$, find the opposite of each term.

$$M^{2}+4M-45-M^{2}-\left(-4M\right)-\left(-32\right)$$

The opposite of $-4M$ is $4M$.

$$M^{2}+4M-45-M^{2}+4M-\left(-32\right)$$

The opposite of $-32$ is $32$.

$$M^{2}+4M-45-M^{2}+4M+32$$

Combine $M^{2}$ and $-M^{2}$ to get $0$.

$$4M-45+4M+32$$

Combine $4M$ and $4M$ to get $8M$.

$$8M-45+32$$

Add $-45$ and $32$ to get $-13$.

$$8M-13$$