Simplify (B(x+h)^2-Bx^2)/h

$\frac{B {(x + h)}^{2} - B x^{2}}{h}$

Step 1

Simplify the numerator.

Factor $B$ out of $B {(x + h)}^{2} - B x^{2}$ .

Factor $B$ out of $B {(x + h)}^{2}$ .

$\frac{B ({(x + h)}^{2}) - B x^{2}}{h}$

Factor $B$ out of $- B x^{2}$ .

$\frac{B ({(x + h)}^{2}) + B (- 1 x^{2})}{h}$

Factor $B$ out of $B ({(x + h)}^{2}) + B (- 1 x^{2})$ .

$\frac{B ({(x + h)}^{2} - 1 x^{2})}{h}$

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = x + h$ and $b = x$ .

$\frac{B ((x + h + x) (x + h - x))}{h}$

Simplify.

Add $x$ and $x$ .

$\frac{B ((h + 2 x) (x + h - x))}{h}$

Subtract $x$ from $x$ .

$\frac{B ((h + 2 x) (h + 0))}{h}$

Add $h$ and $0$ .

$\frac{B ((h + 2 x) h)}{h}$

$\frac{B (h + 2 x) h}{h}$

Step 2

Simplify terms.

Cancel the common factor of $h$ .

Cancel the common factor.

$\frac{B (h + 2 x) h}{h}$

Divide $B (h + 2 x)$ by $1$ .

$B (h + 2 x)$

Apply the distributive property.

$B h + B (2 x)$

Rewrite using the commutative property of multiplication.

$B h + 2 B x$

Simplify (B(x+h)^2-Bx^2)/h

Related Questions

Support LCMGCF.com by disabling your adblocker.