Question

Разложите на множители:а) (x+1)²-4x²; б) x²+2xy+y²-1 в) (a - 4)²-16; г) p²-2pq+q²-4; д) 36m²-(m+9)²; е) 9-x²-2xy-y²; ж) 81q²-(p+6q)²; з) 4-a²-2ab-b². ПОМОГИТЕ ПОЖАЛУЙСТА ОЧЕНЬ НАДО

Answer 1

А). (х+1)²-4х²=х²+2х+1-4х²=-3х²+2х+1
б). х²+2ху+у²-1=(х+у)²-1
в). (а-4)²-16=а²-8а+16-16=а²-8а=а(а-8)
г). p²-2pq+q²-4=(p-q)²-4
д). 36m²-(m+9)²=36m²-m²-18m-81=35m²-18-81
е). 9-х²-2ху-у²=9-(х+у)²
ж). 81q²-(p+6q)²=81q²-p²-12pq-36q²=45q²-12pq-p²
з). 4-а²-2ab-b²=4-(a+b)².

Answer 2

а) (x+1)²-4x²: To factorize (x+1)²-4x², we can use the difference of squares formula, which states that a² - b² can be factored as (a+b)(a-b). In this case, let's consider (x+1) as a and 2x as b. Applying the formula, we have:

(x+1)²-4x² = [(x+1) + 2x][(x+1) - 2x] = (3x+1)(-x+1)

б) x²+2xy+y²-1: To factorize x²+2xy+y²-1, we can rewrite it as a perfect square trinomial. The given expression can be written as (x+y)² - 1. Now, we can apply the difference of squares formula again:

(x+y)² - 1 = [(x+y) + 1][(x+y) - 1] = (x+y+1)(x+y-1)

в) (a - 4)² - 16: To factorize (a - 4)² - 16, we can again use the difference of squares formula. Let's consider (a - 4) as a and 4 as b. Applying the formula, we have:

(a - 4)² - 16 = [(a - 4) + 4][(a - 4) - 4] = (a)(a - 8)

г) p² - 2pq + q² - 4: To factorize p² - 2pq + q² - 4, we can rewrite it as a perfect square trinomial. The given expression can be written as (p - q)² - 4. Now, we can apply the difference of squares formula:

(p - q)² - 4 = [(p - q) + 2][(p - q) - 2] = (p - q + 2)(p - q - 2)

д) 36m² - (m + 9)²: To factorize 36m² - (m + 9)², we can again use the difference of squares formula. Let's consider 6m as a and (m + 9) as b. Applying the formula, we have:

36m² - (m + 9)² = [(6m) + (m + 9)][(6m) - (m + 9)] = (7m + 9)(5m - 9)

е) 9 - x² - 2xy - y²: To factorize 9 - x² - 2xy - y², we can rewrite it as a difference of squares. The given expression can be written as (3 - x - y)(3 + x + y).

ж) 81q² - (p + 6q)²: To factorize 81q² - (p + 6q)², we can again use the difference of squares formula. Let's consider 9q as a and (p + 6q) as b. Applying the formula, we have:

81q² - (p + 6q)² = [(9q) + (p + 6q)][(9q) - (p + 6q)] = (p + 15q)(-p + 3q)

з) 4 - a² - 2ab - b²: To factorize 4 - a² - 2ab - b², we can rewrite it as a difference of squares. The given expression can be written as (2 - a - b)(2 + a + b).

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