Simplify Using Identity Simplify \[ 0.76 \times 0.76 + 2 \times 0.76 \times 0.24 + 0.24 \times 0.24 \] Solution: Using identity: \[ a^2 + 2ab + b^2 = (a+b)^2 \] \[ 0.76 \times 0.76 + 2 \times 0.76 \times 0.24 + 0.24 \times 0.24 \] \[ = (0.76)^2 + 2(0.76)(0.24) + (0.24)^2 \] \[ […]
Simplify the following : 0.76×0.76 + 2×0.76×0.24 + 0.24×0.24 Read More »
Simplify Using Identity Simplify \[ 322 \times 322 – 2 \times 322 \times 22 + 22 \times 22 \] Solution: Using identity: \[ a^2 – 2ab + b^2 = (a-b)^2 \] \[ 322 \times 322 – 2 \times 322 \times 22 + 22 \times 22 \] \[ = (322)^2 – 2(322)(22) + (22)^2 \] \[
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Simplify Using Identity Simplify \[ 175 \times 175 + 2 \times 175 \times 25 + 25 \times 25 \] Solution: Using identity: \[ a^2 + 2ab + b^2 = (a+b)^2 \] \[ 175 \times 175 + 2 \times 175 \times 25 + 25 \times 25 \] \[ = (175)^2 + 2(175)(25) + (25)^2 \] \[
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Evaluate Using Identity Evaluate Using Identity \[ 117 \times 83 \] Solution: Using identity: \[ (a+b)(a-b)=a^2-b^2 \] \[ 117 \times 83 = (100+17)(100-17) \] \[ = (100)^2 – (17)^2 \] \[ = 10000 – 289 \] \[ = 9711 \] Next Question / Full Exercise
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Evaluate Using Identity Evaluate Using Identity \[ 991 \times 1009 \] Solution: Using identity: \[ (a-b)(a+b)=a^2-b^2 \] \[ 991 \times 1009 = (1000-9)(1000+9) \] \[ = (1000)^2 – (9)^2 \] \[ = 1000000 – 81 \] \[ = 999919 \] Next Question / Full Exercise
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Evaluate Using Identity Evaluate Using Identity \[ (0.98)^2 \] Solution: Using identity: \[ (a-b)^2 = a^2 – 2ab + b^2 \] \[ (0.98)^2 = (1-0.02)^2 \] \[ = (1)^2 – 2(1)(0.02) + (0.02)^2 \] \[ = 1 – 0.04 + 0.0004 \] \[ = 0.9604 \] Next Question / Full Exercise
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Evaluate Using Identity Evaluate Using Identity \[ (399)^2 \] Solution: Using identity: \[ (a-b)^2 = a^2 – 2ab + b^2 \] \[ 399^2 = (400-1)^2 \] \[ = (400)^2 – 2(400)(1) + (1)^2 \] \[ = 160000 – 800 + 1 \] \[ = 159201 \] Next Question / Full Exercise
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Evaluate Expression Evaluate \[ (1.5x^2 – 0.3y^2)(1.5x^2 + 0.3y^2) \] Solution: Using identity: \[ (a-b)(a+b)=a^2-b^2 \] \[ (1.5x^2 – 0.3y^2)(1.5x^2 + 0.3y^2) \] \[ = (1.5x^2)^2 – (0.3y^2)^2 \] \[ = 2.25x^4 – 0.09y^4 \] Next Question / Full Exercise
Evaluate : (1.5x^2 – 0.3y^2)1.5x^2 + 0.3y^2) Read More »
Evaluate Expression Evaluate \[ (a – 0.1)(a + 0.1) \] Solution: Using identity: \[ (a-b)(a+b)=a^2-b^2 \] \[ (a – 0.1)(a + 0.1) \] \[ = a^2 – (0.1)^2 \] \[ = a^2 – 0.01 \] Next Question / Full Exercise
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Evaluate Expression Evaluate \[ (a^2b – b^2a)^2 \] Solution: Using identity: \[ (a-b)^2 = a^2 – 2ab + b^2 \] \[ (a^2b – b^2a)^2 \] \[ = (a^2b)^2 – 2(a^2b)(b^2a) + (b^2a)^2 \] \[ = a^4b^2 – 2a^3b^3 + a^2b^4 \] Next Question / Full Exercise
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