Question

please solve the above sum​

Answer 1

Answer:

Formula:-

$\mathtt \purple{ 1)(a + b)(a - b) = {a}^{2} - {b}^{2} }$

$\mathtt \purple{ 2)(x + a)(x + b) = {x}^{2} + (a + b)x + ab}$

$\mathtt \purple{3) {(a - b)}^{2} = {a}^{2} - 2ab + {b}^{2} }$

Solution:-

$\mathtt{1)117 \times 83}$

$\mathtt{ = 100 + 17 \times 100 - 17}$

$\mathtt{ = {(100)}^{2} - {(17)}^{2} }$

$\mathtt{ = 10000 - 289}$

$\mathtt{ = 9711}$

$\mathtt{2)(a - 0.1)(a + 0.2)}$

$\mathtt{ = {(a)}^{2} + ( - 0.1 + 0.2)a + ( - 0.1) (0.2)}$

$\mathtt{ = {a}^{2} - 0.3a + 0.02 }$

$\mathtt{3)991 \times 1009}$

$\mathtt{ = 1000 - 9 \times 1000 + 9}$

$\mathtt{ = {(1000)}^{2} - {(9)}^{2} }$

$\mathtt{ = 1000000 - 81}$

$\mathtt{ = 999911}$

$\mathtt{ 4) {399}^{2} }$

$\mathtt{ = {(400 - 1)}^{2} }$

$\mathtt{ = {400}^{2} - 2 \times 400 \times 1 + {1}^{2} }$

$\mathtt{ = 160000 - 800 + 1}$

$\mathtt{ = 159201}$

Factorise using identities

$\mathtt{1) {9x}^{2} - 12xy + {4y}^{2} }$

$\mathtt{ = {3x}^{2} - 2 \times 3x \times 2y + {2y}^{2} }$

$\mathtt{ = ({3x}- 2y)^{2} }$

$\mathtt{ = (3x - 2y)(3x - 2y)}$

$\mathtt{2)16 {x}^{2} + 40xy + {25y}^{2} }$

$\mathtt{ = {4x}^{2} + 2 \times 4x \times 5y + {5y}^{2} }$

$\mathtt{ = {(4x + 5y)}^{2} }$

$\mathtt{ = (4x + 5y)(4x + 5y)}$

Step-by-step explanation:

I hope this helps you mate.

Answer 2

Step-by-step explanation:

1) 117 × 83

$(100 + 17) \times (100 - 17) \\ = {100}^{2} \times {17}^{2} \\ = 10000 - 289 \\ = 9711$

3) 991 × 1009

$(1000 - 9) \times (100 + 9) \\ = {(1000)}^{2} - {(9)}^{2} \\ = 1000000 - 81 \\ = 999919$

4) 399²

${(399)}^{2} = {(400 - 1)}^{2} \\ = {(400)}^{2} - 2(400 \times 1) + {1}^{2} \\ = 160000 - 800 + 1 \\ = 159201$

5) a) 9x² - 12xy + 4y²

$9 {x}^{2} - 12xy + 4 {y}^{2} \\ = {(3x)}^{2} - 2 \times 3x \times 2y + {(2y)}^{2} \\ = {(3x - 2y)}^{2} \\ = (3x - 2y)(3x - 2y)$

b) 16x² + 40xy + 5y²

$16 {x}^{2} + 40xy + 25 {y}^{2} \\ = {(4x)}^{2} + 2 \times 4x \times 5y + {(5y)}^{2} \\ = {(4x + 5y)}^{2} \\ = (4x + 5y)(4x + 5y)$

Hope you get your answers