Question

1)выполните умножения решите плиз А)(3b-2)(4b-2)= Б)(6а+х)(2a-3х)= В)(c+1)(c^2+3c+2)= 2)Размножите на множитель решите плизз А)2х(х-1)-3(х-1)= Б)ab+ac+4b+4c= 3)Упростите выражения решите плизз -0,4а(2а^2+3)(5-3а^2)= 4)Представьте многочлена в виде произведения А)а^2+ab-3a-3b 5)Решите задачу Из квадратного листа фанеры вырезали прямоугольную дощечку, одна из сторон которой на 2 см, другая на 3 см меньше стороны квадрата. Найдите сторону квадратного листа, если его площадь на 24см в квадрате больше площади получившийся дощечки. ^2 значит а во второй

Answer 1

1)
а)(3b-2)(4b-2)=12b²-6b-8b+4=12b²-14b+4
б)(6а+х)(2a-3х)=12a²-18ax+2ax-3x²=12a²-16ax-3x²
в)(c+1)(c^2+3c+2)= с³+3с²+2с+с²+3с+2=с³+4с²+5с+2
2)
2х(х-1)-3(х-1)=(x-1)(2x-3)
ab+ac+4b+4c=(ab+ac)+(4b+4c)=a(b+c)+4(b+c)=(a+4)(b+c)

Answer 2

To solve these algebraic expressions and equations, I'll go step-by-step and provide the solutions.

1) Solve the multiplications:

a) (3b-2)(4b-2) To multiply these binomials, you can use the FOIL method (First, Outer, Inner, Last): (3b-2)(4b-2) = 3b * 4b + 3b * (-2) + (-2) * 4b + (-2) * (-2) = 12b^2 - 6b - 8b + 4 = 12b^2 - 14b + 4

b) (6a+x)(2a-3x) Using the FOIL method again: (6a+x)(2a-3x) = 6a * 2a + 6a * (-3x) + x * 2a + x * (-3x) = 12a^2 - 18ax + 2ax - 3x^2 = 12a^2 - 16ax - 3x^2

c) (c+1)(c^2+3c+2) Using the FOIL method: (c+1)(c^2+3c+2) = c * c^2 + c * 3c + c * 2 + 1 * c^2 + 1 * 3c + 1 * 2 = c^3 + 3c^2 + 2c + c^2 + 3c + 2 = c^3 + 4c^2 + 5c + 2

2) Multiply by the factor:

a) 2x(x-1) - 3(x-1) Distribute the factor to each term: 2x^2 - 2x - 3x + 3 Combine like terms: 2x^2 - 5x + 3

b) ab + ac + 4b + 4c This expression cannot be simplified further as it contains different variables.

3) Simplify the expression:

-0.4a(2a^2+3)(5-3a^2) To simplify, we'll multiply the terms and combine like terms: -0.4a * 2a^2 * 5 + (-0.4a * 2a^2 * (-3a^2)) + (-0.4a * 3 * 5) + (-0.4a * 3 * (-3a^2)) -4a^3 * 5 + 2.4a^5 + (-6a * 5) + 3.6a^3 -20a^3 + 2.4a^5 - 30a + 3.6a^3 2.4a^5 - 16.4a^3 - 30a

4) Factoring the polynomial:

a^2 + ab - 3a - 3b We'll group the terms and factor by grouping: (a^2 + ab) - (3a + 3b) a(a + b) - 3(a + b) (a - 3)(a + b)

5) Solving the problem:

From the given information, we have a rectangular piece of plywood with one side measuring 2 cm less than the square's side and the other side measuring 3 cm less than the square's side. The area of the plywood is 24 cm^2 more than the area of the cutout piece.

Let's assume the side of the square is "a" cm. Then, the dimensions of the rectangular piece are (a - 2) cm and (a - 3) cm.

The area of the square is a^2 cm^2, and the area of the rectangular piece is (a - 2)(a - 3) cm^2.

According to the given information, the area of the plywood is 24 cm^2 more than the area of the cutout piece:

a^2 = (a - 2)(a - 3) + 24

To solve this equation, we'll simplify and solve for "a":

a^2 = a^2 - 5a + 6 + 24 0 = -5a + 30 5a = 30 a = 6

Therefore, the side of the square is 6 cm.

I hope this helps! Let me know if you have any further questions.