Question

Find the product of (2 pq – q2 ) and (3p2

+ 4q) and verify the result when p = 2 and q = -2

STEPS BY STEPS PLEASE​

Answer 1

Step-by-step explanation:

(2pq-q^2)*(3p^2+4q)

=6p^3q+8pq^2-3p^2q^2-4q^3

now, put p=2 and q= -2

=6(2)^3(-2) +8(2)(-2)^2-3(2)^2(-2)^2-4(-2)^3

=-96+64-48-32

=160-80

=80

Answer 2

The given question is we have to find the product of two expressions and to verify the result when p=2 and q=-2.

$(2pq - {q}^{2} ) \: \: \: \: (3 {p}^{2} + 4q)$

let us multiply these two expressions.

we can multiply this by using a distributive law

$(2pq)(3 {p}^{2} ) + 2pq(4q) - {q}^{2}(3 {p}^{2} ) - {q}^{2} (4q)$

multiply the terms in between the addition and subtraction, we get

$(6 {p}^{3} q) + (8 p{q}^{2} ) - 3( {p}^{2} {q}^{2} ) - (4 {q}^{3} )$

The product of the two expressions is the above value.

we have to verify the result with the value.

$(2pq- {q}^{2} )(3 {p }^{2} + 4q) = (6 {p}^{3} q) + (8 p{q}^{2} ) - 3( {p}^{2} {q}^{2} ) - (4 {q}^{3} )$

substitute the values of p and q in the above expressions we get

here p= 2 and q= -2

$((2(2) (- 2)) - {( - 2)}^{2} )(3({2}^{2}) + 4 \times( - 2 )) = (6( {2}^{3}) ( - 2)) + (8 \times 2( { - 2}^{2} ) - 3(( {2}^{2} )( { - 2}^{2} )) - (4( { - 2}^{3} ))$

$(( - 8 )- (4)) (12 - 8) = ( - 96) + (64) - (48) -( - 32) \\ ( - 8 - 4)(4) = ( - 96 + 64 - 48 + 32) \\ - 48 = - 48$

Hence, the final answer is verified by substituting the values on both sides.

Here, the value of p=2 and q=-2.

# spj2

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