(picture) multiplying monomials and binomials

Second option: 81y^4 - 16x^2, the difference of squares

Step-by-step explanation:

(9y^2-4x)(9y^2+4x) is a special product named difference of squares, then we can apply this formula:

(a-b)(a+b)=a^2-b^2, with a=9y^2 and b=4x, then:

(9y^2-4x)(9y^2+4x)=(9y^2)^2 - (4x)^2

(9y^2-4x)(9y^2+4x)=(9)^2 (y^2)^2 - (4)^2 (x)^2

(9y^2-4x)(9y^2+4x)=81y^(2*2) - 16x^2

(9y^2-4x)(9y^2+4x)=81y^4 - 16x^2

answer: the distance

step-by-step explanation:

to calculate the distance d of a line segment with endpoints (x1, y1) and (x2, y2) use the formula d (x2 x1)2 (y2 y1)2. to calculate the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) use the formula

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west