Solve ল কর: (7p + 3q - 5r) ^ 2 - 2(7p + 3q - 5r)(8p - 4q - 5r) + (8p - 4q - 5r) ^ 2 | 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

$$( 7 p + 3 q - 5 r ) ^ { 2 } - 2 ( 7 p + 3 q - 5 r ) ( 8 p - 4 q - 5 r ) + ( 8 p - 4 q - 5 r ) ^ { 2 }$$

Evaluate

$\left(7q-p\right)^{2}$

Solution Steps

Square $7p+3q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-2\left(7p+3q-5r\right)\left(8p-4q-5r\right)+\left(8p-4q-5r\right)^{2}$$

Square $8p-4q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-2\left(7p+3q-5r\right)\left(8p-4q-5r\right)+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Use the distributive property to multiply $-2$ by $7p+3q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}+\left(-14p-6q+10r\right)\left(8p-4q-5r\right)+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Use the distributive property to multiply $-14p-6q+10r$ by $8p-4q-5r$ and combine like terms.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-112p^{2}+8pq+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $49p^{2}$ and $-112p^{2}$ to get $-63p^{2}$.

$$-63p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}+8pq+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $42pq$ and $8pq$ to get $50pq$.

$$-63p^{2}+50pq-70pr+9q^{2}-30qr+25r^{2}+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-70pr$ and $150pr$ to get $80pr$.

$$-63p^{2}+50pq+80pr+9q^{2}-30qr+25r^{2}+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $9q^{2}$ and $24q^{2}$ to get $33q^{2}$.

$$-63p^{2}+50pq+80pr+33q^{2}-30qr+25r^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-30qr$ and $-10qr$ to get $-40qr$.

$$-63p^{2}+50pq+80pr+33q^{2}-40qr+25r^{2}-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $25r^{2}$ and $-50r^{2}$ to get $-25r^{2}$.

$$-63p^{2}+50pq+80pr+33q^{2}-40qr-25r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-63p^{2}$ and $64p^{2}$ to get $p^{2}$.

$$p^{2}+50pq+80pr+33q^{2}-40qr-25r^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $50pq$ and $-64pq$ to get $-14pq$.

$$p^{2}-14pq+80pr+33q^{2}-40qr-25r^{2}-80pr+16q^{2}+40qr+25r^{2}$$

Combine $80pr$ and $-80pr$ to get $0$.

$$p^{2}-14pq+33q^{2}-40qr-25r^{2}+16q^{2}+40qr+25r^{2}$$

Combine $33q^{2}$ and $16q^{2}$ to get $49q^{2}$.

$$p^{2}-14pq+49q^{2}-40qr-25r^{2}+40qr+25r^{2}$$

Combine $-40qr$ and $40qr$ to get $0$.

$$p^{2}-14pq+49q^{2}-25r^{2}+25r^{2}$$

Combine $-25r^{2}$ and $25r^{2}$ to get $0$.

$$p^{2}-14pq+49q^{2}$$

Expand

$p^{2}-14pq+49q^{2}$

Solution Steps

Square $7p+3q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-2\left(7p+3q-5r\right)\left(8p-4q-5r\right)+\left(8p-4q-5r\right)^{2}$$

Square $8p-4q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-2\left(7p+3q-5r\right)\left(8p-4q-5r\right)+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Use the distributive property to multiply $-2$ by $7p+3q-5r$.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}+\left(-14p-6q+10r\right)\left(8p-4q-5r\right)+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Use the distributive property to multiply $-14p-6q+10r$ by $8p-4q-5r$ and combine like terms.

$$49p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}-112p^{2}+8pq+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $49p^{2}$ and $-112p^{2}$ to get $-63p^{2}$.

$$-63p^{2}+42pq-70pr+9q^{2}-30qr+25r^{2}+8pq+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $42pq$ and $8pq$ to get $50pq$.

$$-63p^{2}+50pq-70pr+9q^{2}-30qr+25r^{2}+150pr+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-70pr$ and $150pr$ to get $80pr$.

$$-63p^{2}+50pq+80pr+9q^{2}-30qr+25r^{2}+24q^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $9q^{2}$ and $24q^{2}$ to get $33q^{2}$.

$$-63p^{2}+50pq+80pr+33q^{2}-30qr+25r^{2}-10qr-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-30qr$ and $-10qr$ to get $-40qr$.

$$-63p^{2}+50pq+80pr+33q^{2}-40qr+25r^{2}-50r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $25r^{2}$ and $-50r^{2}$ to get $-25r^{2}$.

$$-63p^{2}+50pq+80pr+33q^{2}-40qr-25r^{2}+64p^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $-63p^{2}$ and $64p^{2}$ to get $p^{2}$.

$$p^{2}+50pq+80pr+33q^{2}-40qr-25r^{2}-64pq-80pr+16q^{2}+40qr+25r^{2}$$

Combine $50pq$ and $-64pq$ to get $-14pq$.

$$p^{2}-14pq+80pr+33q^{2}-40qr-25r^{2}-80pr+16q^{2}+40qr+25r^{2}$$

Combine $80pr$ and $-80pr$ to get $0$.

$$p^{2}-14pq+33q^{2}-40qr-25r^{2}+16q^{2}+40qr+25r^{2}$$

Combine $33q^{2}$ and $16q^{2}$ to get $49q^{2}$.

$$p^{2}-14pq+49q^{2}-40qr-25r^{2}+40qr+25r^{2}$$

Combine $-40qr$ and $40qr$ to get $0$.

$$p^{2}-14pq+49q^{2}-25r^{2}+25r^{2}$$

Combine $-25r^{2}$ and $25r^{2}$ to get $0$.

$$p^{2}-14pq+49q^{2}$$