MATH SOLVE

2 months ago

Q:
# Drag the tiles to the correct boxes to complete the pairs.Match each expression to its equivalent form.

Accepted Solution

A:

Answer:x² - 16 ⇒ (x + 4)(x - 4)(2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1(2x + 3y)² ⇒ 4x² + 12xy + 9y²x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)Step-by-step explanation:* Lets explain how to solve the problem# x² - 16 ∵ x² - 16 is a difference of two squares- Its factorization is two brackets with same terms and different middle signs- To factorize it find the square root of each term∵ √x² = x and √16 = 4∴ The terms of each brackets are x and 4 and the bracket have different middle signs ∴ x² - 16 = (x + 4)(x - 4)* x² - 16 ⇒ (x + 4)(x - 4)# (2x + 1)³- To solve the bracket we will separate (2x + 1)³ to (2x + 1)(2x + 1)²∵ (2x + 1)² = (2x)(2x) + 2(2x)(1) + (1)(1) = 4x² + 4x + 1∴ (2x + 1)³ = (2x + 1)(4x² + 4x + 1)∵ (2x + 1)(4x² + 4x + 1) = (2x)(4x²) + (2x)(4x) + (2x)(1) + (1)(4x²) + (1)(4x) + (1)(1)∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 8x² + 2x + 4x² + 4x + 1 ⇒ add like terms∴ (2x + 1)(4x² + 4x + 1) = 8x³ + (8x² + 4x²) + (2x + 4x) + 1∴ (2x + 1)(4x² + 4x + 1) = 8x³ + 12x² + 6x + 1∴ (2x + 1)³ = 8x³ + 12x² + 6x + 1* (2x + 1)³ ⇒ 8x³ + 12x² + 6x + 1# (2x + 3y)² ∵ (2x + 3y)² = (2x)(2x) + 2(2x)(3y) + (3y)(3y)∴ (2x + 3y)² = 4x² + 12xy + 9y²* (2x + 3y)² ⇒ 4x² + 12xy + 9y²# x³ + 8y³∵ x³ + 8y³ is the sum of two cubes- Its factorization is binomial and trinomial- The binomial is cub root the two terms∵ ∛x³ = x and ∛8y³ = 2y∴ The binomial is (x + 2y)- We will make the trinomial from the binomial- The first term is (x)² = x²- The second term is (x)(2y) = 2xy with opposite sign of the middle sign in the binomial- The third term is (2y)² = 4y²∴ x³ + 8y³ = (x + 2y)(x² - 2xy + 4y²)* x³ + 8y³ ⇒ (x + 2y)(x² - 2xy + 4y²)