What is (2p+q)(p-2q+3r)-(p-3q)(-3p+q-2r) ?

The solution to (2p+q)(p-2q+3r)-(p-3q)(-3p+q-2r) is 5p^2-13pq+8pr+q^2-3qr

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

simplify (2p+q)(p-2q+3r)-(p-3q)(-3p+q-2r)

simplify

(2 p + q) (p - 2 q + 3 r) - (p - 3 q) (- 3 p + q - 2 r)

5 p^{2} - 13 pq + 8 p r + q^{2} - 3 q r

Solution steps

(2 p + q) (p - 2 q + 3 r) - (p - 3 q) (- 3 p + q - 2 r)

Expand

(2 p + q) (p - 2 q + 3 r) : 2 p^{2} - 3 pq + 6 p r - 2 q^{2} + 3 q r

= 2 p^{2} - 3 pq + 6 p r - 2 q^{2} + 3 q r - (p - 3 q) (- 3 p + q - 2 r)

Expand

- (p - 3 q) (- 3 p + q - 2 r) : 3 p^{2} - 10 pq + 2 p r + 3 q^{2} - 6 q r

= 2 p^{2} - 3 pq + 6 p r - 2 q^{2} + 3 q r + 3 p^{2} - 10 pq + 2 p r + 3 q^{2} - 6 q r

Group like terms

= 2 p^{2} + 3 p^{2} - 3 pq - 10 pq + 6 p r + 2 p r - 2 q^{2} + 3 q^{2} + 3 q r - 6 q r

Add similar elements:

2 p^{2} + 3 p^{2} = 5 p^{2}

= 5 p^{2} - 3 pq - 10 pq + 6 p r + 2 p r - 2 q^{2} + 3 q^{2} + 3 q r - 6 q r

Add similar elements:

- 3 pq - 10 pq = - 13 pq

= 5 p^{2} - 13 pq + 6 p r + 2 p r - 2 q^{2} + 3 q^{2} + 3 q r - 6 q r

Add similar elements:

6 p r + 2 p r = 8 p r

= 5 p^{2} - 13 pq + 8 p r - 2 q^{2} + 3 q^{2} + 3 q r - 6 q r

Add similar elements:

- 2 q^{2} + 3 q^{2} = q^{2}

= 5 p^{2} - 13 pq + 8 p r + q^{2} + 3 q r - 6 q r

Add similar elements:

3 q r - 6 q r = - 3 q r

= 5 p^{2} - 13 pq + 8 p r + q^{2} - 3 q r

\frac{lo g _{a^{2}} ( b )}{( lo g _{a} ( b ^{2} ) )}

2 lo g_{10} (x^{5})

\frac{\frac{143}{2}}{x} - \frac{1}{4} - \frac{1}{12}

80 - 4 x

4 \frac{( 2 x - 3 )}{3} - 2 \frac{( 3 x + 3 )}{5}

What is (2p+q)(p-2q+3r)-(p-3q)(-3p+q-2r) ?
The solution to (2p+q)(p-2q+3r)-(p-3q)(-3p+q-2r) is 5p^2-13pq+8pr+q^2-3qr