Question

1) (a+7)²+(a-2)×(a+5)-7a 2) (a-6)²+(a+3)×(a-5)+7

Answer 1

1)а²+14а+49+а²+5а-2а-10-7а=2а²+10а+39

2)а²-12а+36+а²-5а+3а-15+7=2а²-14а+23

Answer 2

Let's simplify the given expressions step by step:

1. (a + 7)² + (a - 2) × (a + 5) - 7a

Expanding the first term using the formula (a + b)² = a² + 2ab + b²:

= (a² + 2(7)(a) + 7²) + (a - 2) × (a + 5) - 7a = (a² + 14a + 49) + (a - 2)(a + 5) - 7a

Using the distributive property to expand (a - 2)(a + 5):

= a² + 14a + 49 + (a² + 5a - 2a - 10) - 7a = a² + 14a + 49 + a² + 3a - 10 - 7a

Combining like terms:

= (a² + a²) + (14a + 3a - 7a) + (49 - 10) = 2a² + 10a + 39

So, the simplified expression is 2a² + 10a + 39.

2. (a - 6)² + (a + 3) × (a - 5) + 7

Expanding the first term using the formula (a - b)² = a² - 2ab + b²:

= (a² - 2(6)(a) + 6²) + (a + 3) × (a - 5) + 7 = (a² - 12a + 36) + (a + 3)(a - 5) + 7

Using the distributive property to expand (a + 3)(a - 5):

= a² - 12a + 36 + (a² - 5a + 3a - 15) + 7 = a² - 12a + 36 + a² - 2a - 15 + 7

Combining like terms:

= (a² + a²) + (-12a - 2a) + (36 - 15 + 7) = 2a² - 14a + 28

So, the simplified expression is 2a² - 14a + 28.