Question

A) (4x + 6)^2=b) (x^2 + 2p)^3 =B) (x - 8)(X + 8) =​

Answer 1

Відповідь:

А) 16$x^{2}$+48x+36

B) $x^{2}$-64

b)$x^{6} +6x^{4} p+12x^{2} p^{2} +8p^{3}$

Пояснення:

Answer 2

A) To simplify the expression (4x + 6)^2, we can apply the formula for squaring a binomial:

(a + b)^2 = a^2 + 2ab + b^2.

In this case, a = 4x and b = 6. Substituting these values into the formula, we get:

(4x + 6)^2 = (4x)^2 + 2(4x)(6) + 6^2 = 16x^2 + 48x + 36.

Therefore, the simplified form of (4x + 6)^2 is 16x^2 + 48x + 36.

B) To simplify the expression (x^2 + 2p)^3, we can apply the formula for cubing a binomial:

(a + b)^3 = a^3 + 3a^2b + 3ab^2 + b^3.

In this case, a = x^2 and b = 2p. Substituting these values into the formula, we get:

(x^2 + 2p)^3 = (x^2)^3 + 3(x^2)^2(2p) + 3(x^2)(2p)^2 + (2p)^3 = x^6 + 6x^4p + 12x^2p^2 + 8p^3.

Therefore, the simplified form of (x^2 + 2p)^3 is x^6 + 6x^4p + 12x^2p^2 + 8p^3.

C) To simplify the expression (x - 8)(x + 8), we can use the formula for multiplying two binomials:

(a + b)(a - b) = a^2 - b^2.

In this case, a = x and b = 8. Substituting these values into the formula, we get:

(x - 8)(x + 8) = x^2 - 8^2 = x^2 - 64.

Therefore, the simplified form of (x - 8)(x + 8) is x^2 - 64.