Question

Разложите на множители способом группировки a) 3(x-3)-7x(x-3)б) (5+m)(n-2)-(2m+3)(2-n)в) x(b+c)+5b+5cг)4x-4y+ax-ayд) x⁴-8x³+6x-48

Answer 1

Ответ:

Объяснение:

смотри фото

Answer 2

a) 3(x-3) - 7x(x-3)

To factorize this expression using grouping, we can first identify the common factor between the terms. In this case, the common factor is (x-3).

So, we can rewrite the expression as:

3(x-3) - 7x(x-3)

Now, we can apply the distributive property to factor out the common factor:

= (3 - 7x)(x-3)

Therefore, the factored form of the expression 3(x-3) - 7x(x-3) is (3 - 7x)(x-3).

b) (5+m)(n-2) - (2m+3)(2-n)

To factorize this expression using grouping, we can first identify the common factor between the terms. In this case, there is no common factor between the terms.

So, we can rewrite the expression as:

(5+m)(n-2) - (2m+3)(2-n)

Now, we can apply the distributive property to expand the expression:

= 5n + mn - 10 - 2m - 2n + 4m + 6 - 3(2-n)

= 5n + mn - 2n - 10 + 4m + 6 - 6 + 3n

= mn + 5n - 2n + 4m + 3n - 10 + 6 - 6

= mn + 6n + 4m - 10

Therefore, the factored form of the expression (5+m)(n-2) - (2m+3)(2-n) is mn + 6n + 4m - 10.

c) x(b+c) + 5b + 5c

To factorize this expression using grouping, we can first identify the common factor between the terms. In this case, there is no common factor between the terms.

So, we can rewrite the expression as:

x(b+c) + 5b + 5c

Now, we can apply the distributive property to expand the expression:

= xb + xc + 5b + 5c

= xb + 5b + xc + 5c

= (x + 5)(b + c)

Therefore, the factored form of the expression x(b+c) + 5b + 5c is (x + 5)(b + c).

d) 4x - 4y + ax - ay

To factorize this expression using grouping, we can first identify the common factor between the terms. In this case, there is no common factor between the terms.

So, we can rewrite the expression as:

4x - 4y + ax - ay

Now, we can group the terms with common variables:

= (4x + ax) - (4y + ay)

= x(4 + a) - y(4 + a)

= (4 + a)(x - y)

Therefore, the factored form of the expression 4x - 4y + ax - ay is (4 + a)(x - y).

e) x⁴ - 8x³ + 6x - 48

To factorize this expression, we can first look for any common factors. In this case, there is no common factor among the terms.

So, we can try factoring by grouping. Let's group the terms:

= (x⁴ - 8x³) + (6x - 48)

Now, we can factor out the common factors from each group:

= x³(x - 8) + 6(x - 8)

Notice that we have a common factor of (x - 8) in both terms.

= (x³ + 6)(x - 8)

Therefore, the factored form of the expression x⁴ - 8x³ + 6x - 48 is (x³ + 6)(x - 8).