Question

A)x²-12x+36 б) 16b²-8b+1 в)9-6b+b² г)4y²+4y+1

Answer 1

a). x² - 12x + 36 = x² - 2·6·x + 6² = (x - 6)² = (6 - x)²;

б). 16b² - 8b + 1 = (4b)² - 2·4b·1 + 1² = (4b - 1)² = (1 - 4b)²;

в). 9 - 6b + b² = b² - 2·3·b + 3² = (b - 3)² = (3 - b)²;

г). 4y² + 4y + 1 = (2y)² + 2·2y·1 + 1² = (2y + 1)²;

Answer 2

Let's analyze each expression:

a) x² - 12x + 36

This is a quadratic trinomial in the form of (x - a)², where "a" is a constant. To find "a," we take half of the coefficient of the linear term (-12x) and square it.

In this case, "a" is half of -12, which is -6, and (-6)² equals 36. So, the expression can be factored as (x - 6)².

b) 16b² - 8b + 1

This is also a quadratic trinomial, and it appears to be in the form of (4b - 1)².

To check this, let's find the square of the first term (4b) and see if it matches the expression:

(4b)² = 16b² (4b - 1)² = (4b)² - 2(4b)(1) + (1)² = 16b² - 8b + 1

The expression is indeed in the form (4b - 1)².

c) 9 - 6b + b²

This is a quadratic trinomial in the form of (b - a)². To find "a," we take half of the coefficient of the linear term (-6b) and square it.

In this case, "a" is half of -6, which is -3, and (-3)² equals 9. So, the expression can be factored as (b - 3)².

d) 4y² + 4y + 1

This is a quadratic trinomial, and it appears to be in the form of (2y + 1)².

To check this, let's find the square of the first term (2y) and see if it matches the expression:

(2y)² = 4y² (2y + 1)² = (2y)² + 2(2y)(1) + (1)² = 4y² + 4y + 1

The expression is indeed in the form (2y + 1)².

So, the factored forms of the given expressions are:

a) (x - 6)² b) (4b - 1)² c) (b - 3)² d) (2y + 1)²